;lements of logic 



\ 



s 



By CARDINAL MERCK 





Class _£ 
Book._ 



: 



CopyrigM^ .. 



COPYRIGHT DEPOSm 



Digitized by the Internet Archive 
in 2011 with funding from 
The Library of Congress 



http://www.archive.org/details/elementsoflogicOOmerc 



ELEMENTS OF LOGIC 



BY 

His Eminence Cardinal Mercier 



-*- 



THE THIRD EDITION 

Translated by 

EWAN MACPHERSON 



* 



NEW YORK 

THE MANHATTANYTLLE PRESS 

1912 



y\s 



V 



2ftbU ©natal 

Remigius Lafort, D.D. 



Censor 



imprimatur 



John Cardinal Farley 

Archbishop of New York 



LC Control Number 



tmp96 026019 



Copyright 1912 
The Manhattanville Press 

o I 



\'<>\Y 



INTRODUCTION 

1. Definition of Logic. — Logic is the systematic study of the 
order to be observed in judging, reasoning, and other processes 
of thought in order to arrive at the knowledge of truth. This' 
definiti< >n sh< iws us : 

( 1 ) the materials (material cause) of the logical order; 

(2) their elaboration (formal cause) ; 

(3) the purpose of this elaboration (final cause). 

2. Materials of Logical Order. — In some sense, these materials 
are acts of the mind, like apprehension, judgment, ratiocination 
(reasoning) ; but strictly speaking, only apprehensions are the 
material object of logical order (3). 

(1) By apprehension the mind represents to itself one thing 
or many things, without either affirming or denying anything. 
Concepts, the product of apprehension, are expressed by names 
or terms. 

(2) To establish a relation of identity or non-identity, of agree- 
ment or non-agreement, between the objects of two concepts, in 
affirming or denying one object of another is to judge. A judg- 
ment is expressed in a proposition. 

(3) To reason is to combine two or more judgments so as 
to form a new one. The complete ordinary expression of this 
simplest exercise of reasoning is the syllogism. 

3. The Formal Cause of the Logical Order. — The formal 
object of logic, or the point of view from which logic regards 
the acts of the mind, is their adaptability to certain processes of 
thought which are called either particular sciences or philosophy. 
These processes imply stages. The mind must grasp the numer- 
ous aspects of reality one after another before co-ordinating 
the fragmentary explications. Judgment is the first step in com- 
bining ideas; judgments in their turn become the materials of 
reasoning; an isolated piece of reasoning does not suffice to 
produce adequate knowledge of things, but several reasonings 
become materials of a scientific system. This rational arrange- 
ment of ideas constitutes the logical order properly so called : 
""the order which reason constitutes for its own acts". 

3 



.__: 



4 LOGIC 

■ 

4. Difference between Psychology and 1 _,xC. — Many differ- 
ent sciences may be concerned with one and the same subject, if 
they study different properties in it, and, consequently, consider 
it from different points of view. They are then said to have a 
common (that is, undetermined) object, but each has its own 
formal (or determined) object. Psychology, too, has in part for 
its (material) object the act of human reason, but it does not 
study them under the same aspect (formal object) as logic does. 
Psychology sees in them vital acts, of which it seeks the nature 
and origin. Logic considers them in so far as they are cognitions 
of objects, objective representations, abstract and universal, fur- 
nishing the matter of the relations which reason formulates in 
judgments and reasonings, and arranges in a scientific system. 

In psychology, as in all the sciences of the real, order is the 
necessary condition of science; but logic has this order for its 
object. Its proper object is the form itself of this scientific con- 
struction. 

5. Final Cause of Logical Order. — The systematization of the 
.process of reasoning has an ulterior aim: to make our knowledge 
true. 

Before explaining how logic directs its operations towards the 
true, it must be recalled that truth and error are qualities of the 
judgment, and not of the concept. As long as we merely speak 
of some one object by itself — e. g., the sun or a chimera — no one 
can say that we speak truly or falsely. Truth or error belongs 
to the statement that the sun exists, that the chimera exists. 1 

Now, how can a science, logic, lead us to the knowledge of the 
truth? Evidently, logic could not in this sense supply the place 
of all the particular sciences. 

Each science enlightens the mind about the particular object 
with which it concerns itself; and consequently, anyone who had 
studied all of them would be marvellously equipped for always 
forming true judgments. 

But, besides this initiation into the whole of truth by the suc- 
cessive and collective study of the particular sciences, there is an 
initiation of another kind, viz., the preparation afforded by a more 
general science. Thought naturally proceeds from the simple to 



1 See General Criteriology, n°. 6. 



INTRODUCTION 5 

the complex. Now simplicity and universality always go to- 
gether in our knowledge. The most general sciences, then, are 
those the object of which is the most simple and, for that reason, 
best enables us to comprehend the more complex objects to which 
it is applicable. 

■Logic is a general science in the sense that ii regulates the con- 
tent of all other sciences and subjects them to its laws in their 
construction. Its object, of extreme simplicity and boundless in 
extent, is the being of reason. 

6. Difference between Logic and Metaphysics. — Another 
science, having all being for its object, also deserves to be called 
a general science, because it rules all knowledge: this is meta- 
physics. Metaphysics and logic are both concerned with all being 
(common material object), but under different aspects (proper 
formal object). The object of metaphysics is real being consid- 
ered formally in its real quiddity, invested with real attributes. 

Logic has for its object the same being, formally considered in 
its mental objectivity, invested with attributes of reason which it 
acquires in thought and in virtue of thought. 

Everything real (existing or possible) is intelligible. Now the 
real, when it becomes the object of a mental conception, inevita- 
bly participates in the attributes which are inherent in the exer- 
cise of thought: as a mental object, it becomes abstract and uni- 
versal. Between abstract, universal objects relations are estab- 
lished which under the concrete and particular conditions of ex- 
istent things are impossible : such a mental object becomes the 
attribute of another object of thought which plays the part of 
subject in regard to the former; the content and extension of 
ideas give rise to relations of identity or of exclusion; judgments 
are produced, chains of reasoning are forged, and all the while 
the material of these various intellectual operations is being, not 
real being, independent of thought, but the being of reason, i. e., 
being under the aspect and with the characteristics which mental 
conception communicates to it. 

Metaphysics is the universal science of the real. 

Logic is the science of the science of the real. 1 



1 Tin* relations considered by this philosophical discipline are not 
the ontological relations upon which the attention of the mind falls im- 



6 LOGIC 

7. Is Logic to be Considered a Science or an Art? — Is logic a 
speculative or. a practical science? Speculative science stops at 
the knowledge of its object; practical science makes that knowl- 
edge subservient to an ulterior action or work. "The end of the 
speculative is truth ; the end of the operative, or practical, is ac- 
tion." The logician does not study acts of thought merely for the 
disinterested pleasure of knowing their co-ordination; he puts his 
science to the ulterior use of directing mental operations. In this 
sense some hold, and with reason, that logic is a practical science. 
— Others, taking a higher point of view, say that logic is a spec- 
ulative science, because the direction of mental operations is itself 
subordinate to the knowledge of truth. St. Thomas takes this 
view when he says : ' "In speculative matters the rational dialectic 
science is one thing . . . the demonstrative, another." 1 

Logic is also an art, if by this we understand a body of practi- 
cal rules, for the guidance of action. 2 



mediately, the prima: intentiones, objects of a first abstraction, but the 
logical relations springing from the combination of- abstract objects to 
which the reason reflecting returns, sccundce intentiones, objects of second 
abstraction. 

1 Summa Theol, 2a 2* q. 51, art. 2, ad 3. 

2 "Other animals", he says, "are prompted to their acts by a certain 
natural instinct, but man is directed in what he does by the judgment 
of his reason. For this reason various arts serve for the easy and orderly 
execution of human acts. For an art appears to be nothing else but a 
fixed disposition of reason by which human acts arrive at their due end 
by way of calculated means. Now reason not only can direct the acts of 
the subordinate parts, but is also adapted to direct its own function. 
For it is the property of the intellective part to reflect upon itself : the 
intellect understands itself, and in like manner the reasoning faculty can 
reason about its own act. As, therefore, the art of building or of car- 
pentry comes from the fact that the reasoning faculty reasons about the 
act of the hand, and man is thereby enabled to perform acts of this kind 
with ease and with well ordered effort, so, also, there must be some art 
by which the act of the reason itself may be directed, by zuhich man may 
proceed easily and correctly in the very act of reasoning. And this is the 
art of logic, i. e., the rational science. Nor is it rational only because it 
is according to reason, which is a common characteristic of all arts, but 
also because it deals with the very act of the reason as its proper matter. 
And therefore it seems to be the art of arts, because it directs us in the 
act of the reason, from which act all acts proceed." Post. Analyt., lect. I. 



INTRODUCTION 7 

8. Divisions of Logic. — (1) It is usual to divide logic into two 
branches : formal and real logic. This division, which is of rela- 
tively recent date, is very questionable: 

(a) It is obviously inspired by certain arbitrary theories of 
Kant's philosophy. 1 

(b) The questions ordinarily discussed in real logic constitute 
for us the object of a treatise which comes next after psychology, 
and which we call critcriology (science of the criterion of truth 
and certitude), or analysis of certain knowledge. 

(2) Formal logic is generally divided into three parts, treating 
respectively of apprehension, of judgment, and of reasoning. 
This division, which is unimpeachable, is borrowed from the ma- 
terial object of logic. Without rejecting it, we prefer: 

(3) Another division, which squares better with the general 
distribution of every philosophic study 2 and is inspired by the 
study of logical order by its four causes, efficient, material, formal 
and final.'-' 1 

The study of the efficient cause of logic belongs, properly speak- 
ing, to psychology. Here it forms the object of a Preliminary 
Chapter {Chap. I). 

The First Part of the treatise on logic will have for its object 
concepts and terms, the materials of logical order : The Material 
Cause of logical order (Chap. II). 

The Second Part will have for its object the arrangement of 
these materials, their deliberate disposition in judgments, reason- 
ing, system, to secure the knowledge of truth : Formal Cause of 
logical order (Chap. III). 

A concluding chapter will have for its object the employment 
of rational order in the service of science and philosophy: Final 
Cause of logical order (Chap. IV). 4 



1 See Critcriology, n°. 42. 

2 Ci. the beginning of an opusculum in logic reckoned among the 
works of St. Thomas: De totius Logics Aristotclis Summa. Op. XLIV, 
Procemium. Ed. Parm. 

3 Cf. General Metaphysics, fourth part. 

4 These four causes of logical order are mentioned in the definition 
of logic [I] and in the text of St. Thomas: Logic is the "art by which 
the act of the reason itself [material cause] may he directed [formal cause], 
by which man [efficient cause] may proceed easily and correctly in the 
very act of reasoning [final cause]." 



CHAPTER I 

The Efficient Cause of Logical Order 

9. Principles and Nature of the Operations of Reason. — The 

remote principle of the operations of reason is the human sub- 
stance composed of body and soul ; the proximate, or immediate, 
principle is the intellectual faculty. 1 

Psychology teaches us that every act has its origin in the 
senses. While the material thing, which is the object of our sen- 
sations, is always determinate, made of particular matter, en- 
dowed with particular properties, the object of the concept is 
abstract and universal, that is to say, is considered apari from the 
particular attributes which really belong to it in nature (abstra- 
here, to consider separately), and it thereby becomes universal, or 
applicable to an indefinite number of individual subjects. This 
bell, which I see and touch, is made of bronze, it is round in 
shape, it gives a pleasant sound, it is there on my desk at this 
moment as I look at it. All this is determinate. Now I am able 
to think of a bell which abstracts from all these peculiarities, and 
which will serve to represent to me, at least imperfectly, all bells 
of whatsoever material they may be made, whatsoever may be 
their peculiarities of shape or of tone, whatsoever the position in 
space or the moment of time in which they may exist. 

10. Multiplicity of the Operations of Reason. Their Funda- 
mental Identity. — All the operations of reason — apprehension, 
judgment, and reasoning — are at bottom identical; they consist in 
the intuition that something is {quod quid est), but they never- 
theless present different accidental characters which it is of in- 
terest to determine. 

I. Apprehension assumes many formalities. 

(1) When the mind considers an object independently of its 
surroundings, the action is called attention. 

(2) The attention is directed sometimes to a single note in the 
object, independently of those with which it is united, sometimes 



1 See Psychology, n°. 153. 



Till-'. EFFICIENT CAUSE OF LOGICAL ORDER 9 

to the whole collection of notes which constitute the essence of 

the object, but apart from the notes which individualize it in 
reality: such acts of the mind arc called abstraction. 

(3) Abstraction is the basis of generalization. 

( 1 ) Abstraction effects in the mind analysis, i. e., de-composi- 
tion of the notes of the object known. 

(5) When the mind reunites notes previously separated, it 
makes a synthesis. 

(6) When we represent to ourselves two objects in succession 
and perceive a relation between them, the apprehension — or 
rather, the double apprehension— is called comparison. 

(7) The perception of an existing reality is an intuition. We 
call it perception as opposed to the conception of things said to be 
ideal, i. e., things considered apart from their existence. 

(8) When the intelligence has for its object the acts of one's 
own soul, chiefly its spiritual acts, the apprehension takes the 
name of consciousness. 

(9) Distinction is an act by which the mind represents one ob- 
ject to itself as not being the same as a second object. By object 
we are to understand anything that can be the term of an act of 
thought (id quod ob-jicitur cognoscenti). 1 

II. Judgment consists in attributing one object to another, in 
seeing that two objects, previously apprehended, have, or have 
not, anything in common. It is an act of apprehension of which 
the formal object is the identity between the terms of two ante- 
cedent apprehensions (appreheusio complexa, or complexorum — 
complex apprehension, or apprehension of complex things — as 
opposed to simple apprehension, apprehensio incomplexa, or in- 
complex orum) . 

IN. Reasoning is a linking-together of judgments. The rea- 
soning faculty compares with a middle term two extreme 
terms, the. identity of which it does not immediately grasp, with 
the result of seeing, by the aid of this comparison, whether they 
are identical or not. This process is also termed ratiocination. 

The acts of apprehension under their manifold forms, judgment 
and reasoning, fundamentally constitute one and the same act 



1 On the various types of distinction (real, of pure reason, virtual) 
see General Metaphysics, n°. 49. 



10 LOGIC 

— the apprehension or seeing that something is. They depend 
upon a single faculty indifferently called intelligence, understand- 
ing, or reason. 

11. The Abstract Character of Concepts Renders Judgment 
and Reasoning Possible. — Every being which exists in nature 
is itself and no other, it is an incommunicable individuality, and 
it is inconceivable that one real being should be affirmed of an- 
other or attributed to another. Socrates is himself, he is no one 
else; this tree is this tree and no other. 1 

How is it, then, that things are affirmed of one another in our 
judgments? It is because the mind has the power of looking at 
things without their individualizing notes : it abstracts. 

In consequence of this abstractive mode of apprehension, the 
object of the concept is universal; that is to say, it is found, or 
can be found, in many other individuals, and can be attributed to 
them in our judgments (universale in prcedicando) . . - 

Therefore, by means of intellectual abstraction, things can be 
affirmed, or, if we may so express it, are predicable, of one an- 
other. Thanks to this power of abstraction, our notions of beings 
as they are, are attributable to a whole species-, a whole genus; in 
other words they reproduce characteristics of classes — i. e., of 
genera and species. Abstraction makes reasoning possible ; for 
reasoning, as we shall see later, supposes a universal middle term, 
and universality follows abstraction — abstrahi ad quod sequitur 
intentio universalitatis. 



1 See General Metaphysics. "Particulars are not predicated of other 
[objects], but other [objects are predicated] of them." Aristotle, Prior 
Analytics, I, 27. 



CHAPTER II 

The Matter or Material Cause of Logical Order 

12. Object and Division of Chapter II. — By the matter or 

material cause of logical order we mean what this order consists 
of (id ex quo aliquid fit) the materials to be used in constitut- 
ing it. 

The elementary materials are concepts (Article I) and terms 
(Article II). 

Article I will treat of: the concept, its object, its properties 
(§1); the division of concepts (§2). Article II will have a 
parallel division. 

ARTICLE I. 

Concepts. 

§ 1. The Concept, its Object, its Properties 

13. The Concept from the Logical Point of View. — From the 

logical point of view (4) the concept is an element of judgment: 
it is adapted to the role of subject or of predicate, in a proposition, 
notio subjicibilis vel prcedicabilis in enitntiatione. In fact, judg- 
ment is the central act of the understanding: the apprehension 
prepares the elements of the judgment, as reasoning forms a 
new judgment by means of judgments already known. 

By logical concepts, then, we mean the object conceived which 
is enunciated of another and that of which it is enunciated. The 
connection of these two concepts, the copula, is made with the 
verb to be. 

The two concepts, the subject (id quod est sub jec turn attri- 
bution* vel prccdicationi) and the predicate or attribute (id quod 
pra-dicatur vel attribuitur ) are called the terms {termini) of the 
proposition ; they are in fact its extreme points or limits. 

14. What Has Logic to do with the Act of Mere Apprehen- 
sion? — Logic is concerned with the acts of the reasoning faculty in 

11 



12 LOGIC 

so far as it can direct them towards what is true. Now we have 
seen that truth and error appertain to judgment, and not to mere 
apprehension (5). What, then, has logic to do with the study 
of concepts? — They concern it in so far as they furnish the 
matter of true judgments and occasion erroneous judgments. 

15. Logical Problems Arising Out of the Act of Mere 
Apprehension. — The concept can have nothing to do with logic 
except either as subject or as predicate. 

I. In the last analysis, but only in the last analysis, the sub- 
ject of the proposition is always individual. To be sure the 
proposition can have as its subject — indeed often has — an abstract 
type, but in such a case this is the predicate of an antecedent 
subject. The reason of this is twofold: 

(a) Psychological: The first object of thought is taken from 
sensible experience, which is incapable of seizing anything but 
an individual and concrete reality. 

(b) Ontological: Only the individual is, rigorously, a subject. 
Aristotle calls itirpur-n ofola, first substance. For, on the one hand, 
it is not attributable to any antecedent subject. Individuality 
is in fact incommunicable to something else : . Socrates is Socrates, 
he is identified only with himself. 1 On the other hand this first 
substance is the subject of abstract and universal concepts which 
•can be attributed to it on various grounds. 2 

Take the proposition: Snow melts in the sun. Snozu is an 
abstract subject. — But what is snow? Something white which 
I see falling in light flakes, and which I feel to be cold to the 
touch. This thing that is white to the sight, cold to the hands, 
and falls in light flakes, is some snow. This something which 
our senses perceive as white, cold, light, is a first subject; of 
this first subject, some snow is predicated. Snow then becomes 
the subject of a further predicate, the property of melting in the 
sun. 

An examination of the terms of a proposition brings us face 



1 Cf. General Metaphysics, n°. 46. 

2 "Of all things that are, some are such that they cannot be truly 
predicated of any other, as Cleon and Callias, both a singular thing and 
something that is subjected only to the senses, but other things can be 
predicated of them ; for either of these [sc. Cleon and Callias] is a man 
and an animate being." Aristotle, Prior Anal., I, 27. 



THE M \ T l ER OR MATERIAL CAUSE OF LOGICAL < iRDER 13 

to face with a first term which is by its origin an individual subject 
(r65e n) and to which our thought refers all its predicates. 

The individual subject being disposed of, there remains the 
predicate. 

II. The predicate is the object of two principal considerations. 

(1) What does it represent, ivhat does it say about the sub- 
ject? — The study of the logical categories, or predicaments. 

(2) Hoie is it connected with the subject / in what manner must 
it be attributed to the subject? — The study of categoremes or 
predicablcs. 

16. Logical Categories or Predicaments. — Obviously, it is out 
of the question to go in detail through all the predicates of the 
judgments which the human mind enunciates under an indefinite 
variety of forms. But Aristotle has essayed to reduce them to 
certain types of attribution, so as to understand what determina- 
tions they 'bring to the subject which experience supplies, each 
type of attribution (typus prcedicationis) constituting a category 
of homogeneous concepts. He recognized the existence of ten 
great kinds of predicates or attributes, the sum of which is 
virtually equivalent to all the range of human thought, and in 
one or other of which it is possible to find a place for any con- 
cept whatsoever. 

What are the ten predicaments or categories ? (1) Substance, 
that is, second or abstract, substance. 

This thing which we perceive as white, cold, light, is some 
snow. Some snow represents, under an abstract form the sub- 
stance to which our senses find attached those accidental deter- 
minations which are expressed by the adjectives white, cold, 
light. When the mind attributes an abstract substance to the 
concrete substance, rbfe n, perceived by the senses, it applies 
to that concrete substance the first category, ij ova la, n tdrl. 

In contradistinction to the individual subject, irpurrt ovala, prima 
substantia, upon which all predicates rest (15), the category of 
substance is called devrtpa ovala, sccunda substantia. The latter, 
indeed, can be the subject of attributes, but it presupposes a 
concrete subject to which it is referred. 

(2) The other nine types of attribution represent accidental 
determination-. 1 



1 On the difference between the substantial quiddity which we take 
hold of by our logical predicates, see General Metaphysics, n os . S3 sq. 



14 LOGIC 

Of these some are inherent in the subject to which the mind 
attributes them; two of them are absolutely inherent in the sub- 
ject considered, the categories of quantity (e. g., two feet long) 
and of quality (e.g., white, learned) ; a third belongs to the sub- 
ject in respect to a being or beings other than itself — the predi- 
cament of relation (e. g., double). 

Certain predicates represent something extrinsic to the sub- 
ject; the predicates of place (e. g., in the public street), of time 
(e. g., yesterday) are borrowed from measure, the one of quan- 
tity, the other of the duration of the subject. 

Action and passion are attributable to the subject because it is 
the principle (origin) of the former and the term, or aim, of 
the latter (e. g., he cuts the stone; the stone is cut). 

The last two categories, the meaning of which has much ex- 
ercised Aristotle's commentators, seem to have been felicitously 
interpreted by the philologist, Max Miiller, who sees in the 
word KeTcrOai, intransitive action, the active intransitive verb (e.g., 
I walk, I am afraid), in £x« v >the passive intransitive state (e. g., I 
am feeling well). 1 

17. The Predicables. — Human thought is abstractive and uni- 
tive. It represents the reality of nature by means of an assem- 
blage of abstract notes susceptible of being universalized. How 
do these notes (predicates) contribute to the formation of a com- 
plete intelligible object (subject) ? What relation exists be- 
tween the subject and the predicate? In other words, by what 
right is the latter "predicated" of the former? 

There are various predicables or modes of predicability: 

(1) Necessary, because essential predicables .—Certain charac- 
teristics constitute the essence of the thing, which makes the thing 
what it is (quod quid est, rb ri t)v efocu), and without which it could 
not exist or be conceived : such are animality and reason in man. 

(2) Necessary, though non-essential predicables. — Other attri- 
butes do not constitute the substance, but necessarily result from 
it. In an invariable manner they interpret — develop — the con- 
stitutive perfection of the subject: these are called its properties 
(proprium, tdwv.). 



1 St. Thomas, In Met, V, lect. 9. 



THE M \T IKK ( >K MATERIAL CAUSE OF LOGICAL ORDER 15 

(3) Contingent or accidental prcdicables. — Others, again, have 
a contingent connection with the essence: these are called contin- 
gent accidents (contingit ut sint, av^t^Ko^ ), or, more briefly, 
accidents.* 

Essential predicables are subdivided: The object of the intelli- 
gence is not the individual essence, but the specific essence repre- 
sented by different abstract and universal concepts. The term 
species (ef5os) designates the sum of the abstract and universal 
notes which constitutes an essence as the human mind knows it. 2 

Certain of these constitutive notes of a species are at the same 
time applicable to other species; these are called generic, they 
constitute the kind, or genus (ytvos) ; some are proper to it 
and differentiate it from other species of the same genus, and 
these form the specific difference (dia<t>op&). 

Hence three distinct essential predicables ; the species and its 
two parts, the genus and the specific difference. 

Add to these three predicables property and accident, and we 
have altogether five predicables, or catagoremes. 

The properties (idiov) are the determinations which, with- 
out being of the essence of the thing, necessarily follow from the 
essence and, consequently, cannot be separated from it. 

A note is said to be proper to a given species when it belongs 
exclusively to that species, universally to all individuals of that 
species, and constantly to each one of them. "Proprium dicitur 
quod convenit soli alicui speciei, omni et semper." 

Thus the radical aptitude for learning letters is proper to man ; 
incorruptibility is proper to immaterial substances ; limitation is 
pre per to creatures. In this, the only rigorous acceptation, prop- 
erty, has the same extension as essence. 

When a characteristic does not combine the three conditions 



1 Evidently, we must take care not to confound the (ontological) 
accident which is contradistinguished from the substance — whether it have 
contingent or necessary attachments to the substance — with the (logical) 
accident which is immediately contradistinguished from the essence on the 
one hand, and, on the other hand, from the accidents called properties. 
What is predicated as accidental of one subject may be predicated 'as 
essential of another. 

2 Species in the logical acceptation here defined must not be con- 
founded with the same term in the sense attached to it by naturalists — 
that of a collection of individuals capable of indefinite reproduction among 
themselves. 



16 LOGIC 

here stated, it is no longer, rigorously speaking, a property ; it is 
no longer co-extensive with essence. 

Nevertheless, though in a lesser sense, it justifies the appella- 
tion when it presents one or two of the three distinctive notes of 
property : A characteristic which belongs exclusively to a specific 
type, even though it do not belong either universally or con- 
stantly to the representatives of the species, is, in this sense, a 
property: thus, it is proper to man to be a physician, to be a 
geometrician. 

Similarly, a characteristic found in all the individuals of a 
species, and always, but not belonging to them exclusively, may 
be called a property : in this sense, says Porphyry, it is proper 
to man to be a two-legged animal. 

Such, too, is a characteristic which is common to all the repre- 
sentatives of the species and to them only, but temporarily : Thus, 
according to Porphyry, it would be proper to mail — to every 
man and to men only — to grow grey in old age. 

The common accidental quality, accident (o-u^e/3i;/c6s as opposed 
to idiov, accidens commune as opposed to proprium), may be de- 
fined in a negative way : the quality which is not a property in 
the strict sense of the word. In a positive way Porphyry defines 
it : An accident is a quality to the presence or absence of which 
the essence of the subject is indifferent (Accidens est quod adest 
et abest praeter subjecti corruptionem). 

The common accidental quality, Porphyry adds, is sometimes 
constant, sometimes belongs to the subject only intermittently. 
We may say of the animal that it sleeps ; black plumage may be 
attributed to the crow constantly. 

From this we see that care must be taken not to confound the 
quality, even the constant quality, with the property. 

The mere observation of facts does not suffice to effect the 
discernment of a property. This discernment, we shall see later, 
forms the object of scientific induction and calls for the employ- 
ment of experimental methods. 

18. Comprehension and Extension of Concepts. — There are 
relations of subordination between various predicables. To under- 
stand these it is necessary to establish two logical properties of 
abstract concepts : their comprehension and their extension. 

The comprehension of an idea is its content, the sum of the 
characteristics or notes which analysis can find in it. Take the 



THE MATTER OR MATERIAL C UJSEOP LOGIC VL ORDER 17 

abstract idea of man. When we consider what this idea repre- 
sents, we find in it different characteristics taken by abstraction 
from the individuals. The extension of an idea is its rang* oi 
applicability, the sum of the subjects to which the abstract idea is 
applied or can be applied, extends or can extend. 

We thus consider the abstract and universal concept as a whole, 
whether metaphysical or logical. Man is a metaphysical whole, 
which comprises corporeality, life, sensibility, reason, as so many 
metaphysical parts. 1 

The idea of man is attributable to all men, past, present, future, 
or merely possible : it forms a logical whole of which men. taken 
distributive^-, are the logical parts. 

The Latin words totus and omnis correspond to the two mem- 
bers of this distinction. 

An idea is more or less comprehensive accordingly as it em- 
braces more or fewer notes. It has greater or less extension ac- 
cordingly as it applies to a greater or smaller number of subjects. 

These two properties of the idea are in inverse ratio to each 
other: the greater the comprehension of an idea, the less its ex- 
tension, and vice versa. 

When we compare two or more ideas in the twofold respect 
of their extension and their comprehension, certain relations are 
seen to arise between them. 

19. Relations of Subordination among- Ideas in Respect of 
Their Extension. — There are degrees in the universality of con- 
cepts; those referable to the same category thus form a logical 
scale. 

On the lowest step we find the individual substance, which is 
not attributable to any subject, and to which all predicates are 
attributed, 

Next above comes the species, which is asserted of the indi- 
viduals. Then the genus, which is asserted of the subordinate 
species and the individuals. 

The genera (kinds) may in their turn be manifold: nearest, or 
immediate, genus; or subordinate genera: highest, or most gen- 
eral genus. 

Porphyry has drawn up a Table showing the essential pred- 
icates of substance and their mutual subordination. 



i Sec General Metaph., no. 48. 



18 LOGIC 

Most general genus . . . Substance 



Difference . Animate 
Subordinate genus . . 



Difference . Corporeal . . . 
Subordinate genus Body 



Living: 



Difference . With feeling . . 
Subordinate genus ..... Animal 



Incorporeal 



Inanimate 



Without feelinp- 



Difference . Rational . . . 
Subordinate genus .... Man 



Irrational 



Individuals 
Some man 
Some horse 


Hypostases 

Socrates 

Bucephalus 


Singulars 
That man 
That horse 



\l \ r fER OR MATER] UL CAUSE OJ LOGK Ai.< IRDER 19 

20. Comparison of Ideas in Respect of Their Comprehension. 
Relations of Identity and Opposition. Two ideas are identical 
or different accordingly as they have the same or a different con- 
tent (the ideas of man and rational animal; of man and animal i. 

( >f nun-identical ideas some are compatible (liquid and sweet) ; 
others, incompati'ble (liquid and solid). 

Opposition, or incompatibility, between two idea- is produced 
in four ways: it is contradictory, privative, contrary, relative. 
1 i The opposition is contradictor}- when the two terms have 
nothing in common; for one of the terms is being, and the other 
is the negative of being. Two ideas, in short, are contradictory 
when one is neither more nor less than the negation of the other 
i ti'hitc and not white, just and not just, etc. ). 

Privation is the negation of a perfection in a subject 
which is naturally fitted to possess it (negatio alicujus forma? in 
subjecto apto nato habere illam) ; thus blindness is the privation 
of sight, death is the privation of life. Privation is not merely 
synonymous with negation or absence; a mineral has no sight, 
but is not deprived of it. 

I Contraries form the two extreme points of a series of 
elements which are joined in the same genus. Suppose, e. g., that 
the degrees of light are mentally arranged in a series, the two 
extreme terms of the series, white and black, are two contraries. 
•There is the opposition of contrariety between things which can- 
not coexist in the same subject. Health and sickness, justice 
and injustice, courage and' timidity, are contraries. 

! "i Relative opposition, or relation, is that between two terms 
either of which needs the other to explain it. Ex.: the ideas 
of father and son. of double and half, of knowledge and the 
object known. 

s; 2. Classification of Concepts 

21. Principal Heads of the Classification of Concepts. — Con- 
cepts, or ideas, are divided: ( 1) in respect of the object which 
the intelligence abstracts from the things to be known; (2) in 
respect of their manner of representing the thing known; (3) 
in respect of their origin or their formation. 

Certain members of these divisions might be placed indif- 
ferently under any of several heads. 



20 LOGIC 

22. In Respect of the Object Abstracted by the Intelligence. 

ideas are divided (1) into transcendental, generic, specific, 
singular ideas. 

This classification is based on the degrees of abstraction of the 
intellectual cognition. 

The idea which represents all the determinations of the object, 
including- those which make it an individuality, is singular. 
Ex. : the ideas of Caesar, of Napoleon, etc. 

The idea which represents the thing- in a more indeterminate 
manner, offering to the mind. only those notes which belong in 
common to individuals of the same species, or to several species 
of the same genus, is either specific or generic, as the case may 
be, but in either case is universal. 

When the idea is still more indeterminate, and the intelligence 
represents things by means of certain characteristics common to 
all being in nature, the idea is called transcendental, ''because 
it transcends every genus, every category" ; the extension of 
this idea goes beyond all the categories. We distinguish six 
transcendental notions: being (ens), thing, one, something, true, 
good. 1 

Remark: When several individual things are considered as 
forming one whole, the idea which represents them is called 
collective; such, e.g., is the idea of a people, an army. The 
collective idea must never be confounded with the universal. 

(2) Into adequate and inadequate ideas. The former make 
known to us all the characteristics which belong to the object — all 
those, at least, which are within the natural range of the in- 
telligence. The latter does not attain this degree of complete- 
ness. 

The inadequate idea is confused, indeterminate, indistinct ; or 
it is clear, determinate, distinct. The confused idea shows us 
the object by means of notes which are insufficient to let us 
distinguish it from every other object, as when I conceive of a 
fish as a creature that swims. The clear and distinct idea may 
include certain notes which are common to several objects, but 
it contains some which belong exclusively to the object to be 
known, and which therefore distinguish it from every other 



1 See General Metaph., n° 39. 



MATTER OR MATERIAL CAUSE OF LOGN \JLORDER -.'1 

object; e.g., when I define the fish as the living creature which 
breathes only through gills. 

(3) Into complex and simple. The idea is complex when it 
embraces several parts each of which by itself can be a predicate, 
as the idea just man. The ideas just and man are simple. 

23. In Respect of the Manner of Representing Their Object, 
idea- are principally divided into concrete and ahstraet, positive 
and negative, proper and analogical idea-. 

i 1 i No concrete idea exists, hut by this name we Improperly 
jiate an idea the object of which is conceived in union with 
mcrete subject, as the idea- white, animal. 

In opposition to this, an idea is said to he abstract when it 
sents a note apart from any concrete subject; e. g., the ideas 
of whiteness, of animalitv. 

In reality the "concrete" idea grows out of an abstractive act; 
the "abstract" idea comes of a second abstraction, and is re- 
flexively abstract. 

(2) The positive idea represents a thing by means of notes 
which really belong to it; as the ideas of light, of life. 

The negative idea makes an object known to us by eliminating 
from the thought notes which the object excludes; as the ideas 
of darkness, of death. 

i 3) The positive idea is proper when it grasps a property, i. e., 
a quality which is distinctive of a being, such as it is positively. 

The analogical idea is that which we form of a being in itself 
inaccessible to the intelligence: to know it, we compare it with 
another being of which we know the properties positively. E. g., 
the Divine life is known to us by analogy with created life; the 
presence of spirits by analogy with the presence of bodies in 
space. 

24. In Respect of Their Origin or Their Formation, cogni- 
tions are immediate or mediate. 

They are immediate or intuitive when the object to be known 
self united with the intelligence or, at least, itself begets in 
the intelligence the representation of what it is. 

When the cognition of the object is dependent upon that of 
another object, the cognition is called mediate. This is proper 
or analogical accordingly as the object which serves as inter- 
mediary is or is not of the same nature as the object to be 
km iwn. 



22 LOGIC 

Mediate cognition is sometimes called ''abstractive," as op- 
posed to ''intuitive'' cognition. 

ARTICLE II. 

" Terms. 

§ 1. The Term, its Objects and Properties 

25. The Object of the Term. — Terms are vocal signs which 
express objects as they are conceived by the intelligence ; they 
are not the expression of subjective concepts as such, or of 
things as they are in nature, but of things as the intelligence 
conceives them; in a word, they designate known objects. "It 
is through the medium of intellectual conception", says St. 
Thomas, "that words are related to the representation of things." 
(Voces referuntur ad res significandas mediante conceptione in- 
tellectus). 1 

The word sun, e. g., does not signify the idea of the sun, but 
the sun itself. And yet that word does not directly designate 
the sun as it is in nature. For it was long supposed that the 
sun was a disc moving around our planet ; now this is not the 
true sun, but only the sun as humanity imagined it before the 
discoveries of Galileo and Copernicus. 

It belongs to psychology to study the nature and functions of 
language. 

26. The Ten Parts of Speech. — As the objects of our thoughts 
can be divided into ten categories, it seems natural to find an 
analogous division in the terms which correspond to our con- 
cepts. Grammarians do, as a matter of fact, distinguish ten 
parts in speech, just as Aristotle had distinguished ten categories 
of thoughts in connection with ten kinds of things known. 

There is, however, no adequate correspondence between the 
categories and the parts of speech. 

The first subject of all logical attributions is what the senses 
perceive in its concrete reality, and which at the outset presents 
itself to the thought in complete indeterminateness, — this some- 
thing, hoc aliquid, this, that. 



1 Summa'Theol.j I, q. 13, a. 1. 



THE M \T I IK ( IE M \TI R] ^.L CAUSE OF LOGICAL ( >RDEB 

Formal determinations which the mind conceives in an abstract 
manner, and which the terms of language express, gradually fill 
up this first indeterminateness. The chief are expressed by the 

substantive, the adjective, and the attributive verb, which con- 
stitute the essential elements of language. 

i 1 i The first determination is the essence, or the very sub- 
stance, of the subject, designated by the noun, or substantive. 
The substantive designates any object which is a substance or 
any quality considered as if it were a substance (man, horse, 
height, whiteness). 

In its first acceptation the noun is abstract and, therefore, 
common. 

Further determinations have individualized its signification and 
made proper nouns out of it. 

(2) Two categories represent determinations inherent in the 
subject: some are qualitative; others, quantitative; these are 
adjectives. 

(3) The attributive verb represents action or passion in 
operation. 

As for the verb to be, it either designates the act of existing 
(I am) or plays a merely copulative part, uniting subject and 
predicate, in which latter character it is implied in every attri- 
butive verb — e. g., I work == I am working. 

It is interesting to note that the results of linguistics agree 
with the study of logical concepts : just as the predicates of 
judgments are abstract, so the roots, or primitive forms, of 
language express abstract ideas. 

§ 2. Classification of Terms 

27. Classification of Terms. — The classification of concepts 
is applied to terms. Let us note a few properties of the latter. 

(1) Terms are common or singular. Common terms are 
transcendental or merely general universal, and these arc generic 
or specific. 

Generic and specific terms are univocal; transcendental terms 
are analogical. 

This distinction is based on another classification of terms. 

(2) Terms are univocal when with a common name they 



24 LOGIC 

designate things to which an essentially identical definition cor- 
responds. E. g., the noun animal is applied to a man and an. ox 
in an identical sense, either of the two being an animate sub- 
stance endowed with feeling. 

Equivocal terms designate with a common name diverse things 
the concepts of which are different. E. g. the noun dog is ap- 
plied to an animal and a constellation. 

Analogical terms designate with the same name things the 
corresponding concepts of which are partly the same and partly 
different. Thus, when we say of bodies and of spirits that they 
occupy a portion of space, the words occupy space have not an 
identical sense in the two cases, but an analogical sense. Analogy 
is expressed by metaphor. 

(3) Terms, like concepts, are simple or complex. 

(4) They are concrete or abstract. The word white is a con- 
crete term ; the word zvhitenesSj an abstract term. 

(5) Terms are positive or negative: e.g., death, immortality. 
—A positive term may convey a negative idea; a negative term, 
a positive idea. 

(6) Terms are direct or reflex: e. g., substance, man, are direct 
terms ; genus, species are reflex. 

(7) Categorematic terms have a complete sense in themselves, 
and can by themselves play the part of subject or attribute (e. g., 
man) ; syncategorematic terms have a complete sense only 
through their union with another term (e.g., none, all). 



CHAPTEE III 

Form \i. ( )ai se of I .ogk u ( >rder. 

28. Preliminary Note.— The orderly arrangement of science 
is accomplished in a progressive way. 

First, the predicate is formally connected with the subject: an 
>f judgment. 

Then, being brought together and combined, the judgments 
produce more complex judgments: reasoning. 

Lastly, several reasonings relating to the same object con- 
tribute to the formation of a logical system: organization of 
science. 

Chapter 111 will consist of three articles corresponding to the 
three stages of logical order. 

Article I, devoted to the study of the judgment and the proposi- 
tion, will be divided into three sections: 

§ 1. Meaning of the judgment and the proposition. 

^ •.'. Judgments and propositions. 

Relations between judgments and propositions. 

ARTICLE I. 

Judgment and Proposition. 

§ I. Meaning of Judgment and of Proposition 

29. The Judgment and the Proposition. — The proposition is 
the expression of the judgment and consists in enunciating 
(asserting) one thing of another. "Propositio est oratio enuncia- 
tiva", dv6((>apuis, says Aristotle. 

All speech signifies something — "omnis oratio est significa- 
tiva." (pdais, <puv)) ff-nfxavTiKr) — but not all speech enunciates some- 
thing. The noun signifies something; it does not enunciate. For 
instance, "prayer" is a noun, it is not an assertion. 1 

"\ first enunciative phrase has the form of an affirmation, 



1 Aristotle, Perihermeneias, c. IV. 



26 LOGIC 

another has the form of a negation; those which do not present., 
this simple character are, nevertheless, all composed of these 
elementary enunciations." 1 The enunciation (or assertion) 
consists of two terms — the subject and attribute — joined by the 
verb to be. 

In view of a property which proceeds from the notion of the 
proposition, we may also define it: a true or false speech. 

30. The Place of the Judgment and of the Proposition in 
Intellectual Life. — Not only is the judgment the central act to- 
wards which all the operations of thought converge, but there 
is in reality no intellectual act. which does not end in judgment. 

Each of the abstractive acts of the intelligence grasps one of 
the attributes of the known object separately — e. g., one quality 
of this tree which my senses perceive, the shape of the trunk or 
of the branches, the roughness of the bark, the color of the 
foliage, and so on. 

But each one of these acts is accompanied by the apprehension 
of something subsisting, of a subject from which I borrow, and 
to which I give back, the abstract attribute. 

To abstract these attributes — the shape, the roughness, the 
color of this tree — is only to attribute them mentally to this. 
indeterminate subject which I am seeking to specify, to say 
within myself that they belong" to it, to judge that a tree is what 
they express. 

The science of language confirms and illustrates the teachings 
of consciousness. 

To create a name (or noun) is, in fact, to apply a concept, 
moulded in the form of language, to some subject designated 
indeterminately by a demonstrative pronoun, this or that. To 
name this animal that which tears to pieces (Vr Ka, lupus, wolf) 
is to apply to the creature an abstract concept, that of the act 
of tearing to pieces. 

§ 2. Judgments and Propositions 

31. General Classification of Propositions. — Simple proposi- 
tions include only their subject, their attribute, and the copulative 

i Ibid,, c. V. 



l-< >RMAL CAUSE OF LOGIC \I. I IRDER 27 

verb; composite, or complex, propositions include ninny simple 
propositiorfs joined together. 

Simple propositions are in their turn divided according to their 
metier, their form, their quantity, their quality. 



I. Classification of Simple Propositions 

32. First Classification of Propositions: According to Their 
Matter. — By matter is meant the terms in their mutual relation, 
hut previous to the effective enunciation which the judgment 
formulates. 

Seme propositions are in necessary nuttier; others ; in contin- 
gent matter. 

A proposition is said to be in necessary matter when the con- 
nection between the two terms absolutely cannot be other thaw 
it is, and is revealed to the intelligence by mere analysis of the 
terms and independently of all experience; as 2+2=4. 

A proposition is said to be in contingent matter when the con- 
nection between the two terms is such as it is, only uppn certain 
conditions realized in contingent existences and cannot, therefore, 
be enunciated without experience; e. g., that water freezes at 0° 
centigrade. 

The judgment in contingent matter with which logic is 
cerned presents, then, a necessity* but a contingent necessity, 
whilst the necessity of the judgment in necessary matter is abso- 
lute. 1 fence judgment in necessary matter must not be con- 
founded with necessary judgment. 

The necessary proposition is knowable by itself, "propositio per 
se nota"; the contingent proposition, on the contrary, is knowable 
dependently upon something other than the mere terms of the 
proposition, "propositio per aliud nota." 

33. Two Kinds of Judgments in Necessary Matter. — I. First 
bud: The connection is necessary because the subject, consid- 
ered in it-, osential elements, is either the same term as the pred- 
icate (identical judgment I, as: a square is an equilateral rectangle ; 



l The particular judgment in contingent matter does nol directly 
belong to the domain of science. Scicntid non est de singularibus. 



28 LOGIC 

2=1—1 ; or includes the predicate, the latter being in this case 
part of the essence of the subject, as : a square is a rectangle; man 
is intelligent. In both cases the comparison of the two terms of 
the judgment reveals to the mind the necessity of their connec- 
tion. 

II. Second kind: The connection between the two terms of 
the judgment is necessary when the predicate necessarily presup- 
poses the subject and, consequently, is not definable without bring- 
ing the essence of the subject into evidence. This case is where 
the predicate is a property (in the rigorous- acceptation) of the 
subject. 

The definition of the predicate (simple or disjunctive), put side 
by side with the essential notion of the subject, brings out the 
necessary connection of the two terms. 

(a) Example of a simple predicate: 

A prime number is one out of which it is impossibLe to form 
several groups each containing the same number of objects. ! 

This definition does not mention as a component part the num- 
ber 5. But if we place the definition on one side, and on the other 
side the result of breaking up the number 5 into two groups of 
two units each and one of one unit, it will then appear that the 
definition of a prime number necessarily applies to the number 5. 
That is, a prime number is not the definition of the number 5, but 
to be prime is one of its properties. 

(b) Example of a disjunctive predicate: Every number is 
either even or odd. 

The attribute even is not essential to number ; it is not even a 
necessary property. Neither is the attribute odd of the essence 
of number or a property of it. The alternative even or odd forms 
no part of the definition of number, but it is a necessary conse- 
quence of that definition. Given that unity is not a number, but 
the principle of numbers, every number is or is not divisible by 2, 
is even or odd. 

The Scholastics, following Aristotle, called the two kinds of 
necessary propositions which we have just been studying, duo 
modi dicendi per se, propositiones per se (two ways of saying by 



1 A prime number is usually denned as one which is divisible only 
by i t - elf and unity. 



I't IRMAL CAUSE OF LOGICAL ORDER 

themselves, propositions by themselves), 3 Ka.6" afod, and op 

to thorn modi dicendi per accidens, propositiones per accidens, 

Kara (TVfxPe^rjKds. 

It must be added that the necessity of the connection becomes 
apparent sometimes immediately, sometimes in a mediate way 
after more i r less laborious analysis. This is an entirely subjec- 
tive affair which nowise affects the nature of the connection. 

34. Synonymous Designations of the Foregoing. — Propositions 
in necessary matter are also called metaphysical and absolute, he- 
cause their objed is metaphysically necessary, independent of the 
conditions inherent in contingent existences, ruder the- 
ignations they are opposed to conditional or physical pr 
ti( ms. 

The former are called pure rational to indicate that reason is of 
itself capable of apperceiving their truth; whilst the knowledge of 
the latter, the experimental, empiric propositions, is subject to a 
verification of fact. 

Lastly, since Kant, the former a"re called a priori; the latter, a 
posteriori; the former, analytic; the latter, synthetic. It is im- 
portant to note care full\ that these expressions are given in the 
Kantian philosophy a special signification which precludes their 
identification with the expressions used by the Scholastics. 

Between the judgments in necessary and in contingent matter 
of the Scholastics and the analytic and synthetic judgments of 
Kant there are fundamental differences which it belongs to cri- 
terii »logy to establish. 

35. Second Classification of Propositions : According to Their 
Form. — /•"<</-/// here means the union of subject and predicate a- it 
is effected in the enunciation of the judgment. 

1 "Per se", says St. Thomas, "is used in a twofold sense. In one 
waj a proposition is said to be per se when its predicate falls within the 
definition of the subject, as: Man is an animal; for annual is contained 
in the definition of man. And because that which is in the definition of 
a tiling is in a way its cause, in these per se propositions the predicate 
i- said to be the cause of the subject. A proposition is also said to be 
per se in another way, when the subject is in the definition of the predi- 
cate, as: The nose is a hook; the number is even. For a hook [in this 
sense] is only a nose with a certain curve, and even is nothing but a 
number which has a half, and in these the subject is the cause of the 
predicate." De annua, bk. II. tect. 14. 



30 LOGIC 

( 1 ) The proposition is affirmative or negative 1 accordingly 
as the mind asserts that the predicate belongs to the subject, and 
consequently must be joined to it (coinpositio) , or not 
( diiisio ). 2 

(2) With the form of judgments must be connected their 
modality, or the particular determination which marks the union 
of predicate and subject. Under this aspect the proposition is 
apodictic 3 empiric, problematic. "Every proposition consists in 
asserting that [something] is contained in, or is necessarily con- 
tained in [something] else, or that it may happen to be con- 
tained. " y 

The apodictic proposition (which we must take care not to con- 
found with the proposition in necessary matter) asserts that the 
predicate necessarily agrees with the subject or is necessarily re- 
pugnant to it. As: There must be a First Cause in the world. 
It is impossible for the world to exist of itself. 

The empiric proposition asserts that the predicate as a matter 
of fact agrees with the subject. As: So and so died yesterday 
morning. 

The problematic proposition, based upon a mere possibility, 4 
asserts in a conjectural way the happening or non-happening- of 
an event which has no natural connection with a determinate 
cause. As : It is possible that so and so may draw the prize. 



1 A negative proposition sometimes has the appearance of an aMrma- 
tive, as : This man lacks generosity — is not generous. Inversely, an ap- 
parently negative proposition may he at bottom affirmative, as : Man is 
not infallible; The world is not infinite. 

- Every proposition which asserts something (P) about a subject (S) 
mentally effects a certain union (composito) of a predicate with a sub- 
ject. Here the belonging or non-belonging in question of the predicate 
and subject is objective. St. Thomas, Periherm., lect. 3. 

"'Prior Analyt., I, 2. 

-* For Aristotle possible here does not mean non-contradictory, but 
contingent. St. Thomas writes in the same sense: "That is called neces- 
sary which in its own nature is determined only to being ; impossible that 
which is determined only to non-being; possible, that which is altogether 
determined to neither, whether it be more inclined to the one than to the 
other, or whether it be ecprally inclined to both, or, as it is expressed in- 
differently contingent [eontingens ad utrumlibet]." In Periherm., lect. 14, 
n. 8. 



F( )k.\l \1. CAUSE < >r L< JGICAL ORDER 31 

36. Logical Value of the Predicate of a Simple Proposition. 
— The comprehension and extension of the predicate are a func- 
tion of the form of the proposition, [n an affirmative proposition 
they are in Inverse ratio to what they arc in a negative. 

(1) In an affirmative proposition the predicate is taken in all 
of its comprehension, although this may be less than that of the 
subject; but only in a part of its extension. All the notes of the 
predicate, taken together or separately, apply to the subject; hut 
ibject need no1 represent, and consequently does not, so far 
as the enunciation goes, represent more than a portion of the 
objects within the extension of the predicate. E. g., when I say, 
log is a vertebrate'*, I mean to assert that the dog has all the 
properties included in the idea vertebrate, collectively < r distrib- 
utively; but nut that there are no other vertebrates hut the dog. 

Then- is, however, this reservation to be made: that in essential 
■definitions, the thing defined and its definition have the same ex- 
tension and the same comprehension. 

I 2 i In a negative proposition, on the contrary, the predicate 
is taken in its whole extension, but only in an indeterminate -part 
of it-, comprehension. E. g., when I say, "The mollusc is not a 
vertebrate", I mean to say that the mollusc is not any one of the 
vertebrate-, because it does not include all the attributes of the 
vertebrates; but that does not prevent its having some of the 
properties which belong to the vertebrates. I exclude all the 
subject- to which the idea i i vertebrate applies, but I need not 
therefore exclude all ' e notes which that idea comprehends. 

37. Third Classification of Propositions: According to Their 
Quantity. — A proposition is universal, singular (or particular), 
indefinite. 

i 1) The universal proposition asserts that an attribute belongs 
to (/// the subjects of an idea or to none of them. As: All men 
are mortal ; No man fatally misses his destiny. 

i 2 i The singular proposition enunciates an attribute of one in- 
dividual. When the subject represents a determinate group of 
individuals, it is collective: in the logical point of view it is of the 
same nature as the singular subject. We also call all those prop- 
ositions particular the subject of which is not universal, whether 
it include many individuals of the same species or only one. As: 
Some men are learned ; the Belgian people is active. 



32 LOGIC 

(3) The indefinite proposition expresses the agreement or non- 
agreement of a predicate and a subject without expressly saying 
whether the subject is taken in all its extension or only in part of 
it. As: They have been unjust in this matter. 

The universal proposition is more important than the particular. 
The former, indeed, contains the latter in its extension; to know 
the former is virtually to know the latter ; but the converse is not 
true. 

38. Fourth Division of Propositions: According to Their 
Quality. — Propositions are true or false accordingly as the con- 
nection which they assert is or is not in agreement with that 
which is. 1 

II. Classification of Composite Propositions 

39. Classification of Complex Propositions. — Rigorously speak- 
ing, a composite, or better, a complex, proposition is an enuncia- 
tion which includes several simple propositions. 

The authors of Port-Royal enumerate six types of proposition 
in which the complexity is manifest, and four in which it is more 
or less latent. We will define them and establish the conditions 
of truth in each. 

I. The first six are the copulative, disjunctive, conditional, 
causal, relative and discrctive. 

(1) The copulative proposition is that which includes many 
subjects and many attributes joined by an affirmative or negative 
conjunction, and or nor: This proposition is true only if its parts 
are true. 

(2) Disjunctive propositions state an incompatibility at the 
same time as an alternative, as : Every free action is morally good 
or bad. 

The condition of. truth in these propositions is that the two 
parts of the disjunction should be mutually opposed and should 
admit of no middle term. 

(3) Conditional propositions consist of two parts connected by 
if; the first, which contains the condition, is called the antecedent; 



1 Many authors call that quality which we have called the form of a 
proposition. In respect to the quality, they say, propositions are affirma- 
tive or negative. — A question of mere words, of very slight importance. 






|( )KM \l. I UJSE < IF LOGIC \I. < >RDER 33 

the second, the consequent. E. g.\ It the soul is spiritual (ante- 
cedent), it is immortal (consequent). 

For the truth of these propositions we have to consider only the 
truth of the consequence: the falsity of both parts does not hinder 
the proposition, as a conditional proposition, from being true. 
!•'.. g. : If the soul of animals were spiritual, it would be immortal. 

(4) The causal proposition contains two propositions joined 
by some word indicating a cause — because, etc. 

Reduplicative propositions also belong to this class. E. g. : 
Evil, as such, is not the object of the will. 

For the truth of these propositions it is not enough that the 
two parts should be true; one part must also be the real cause 
of the other. 

(5) Relative propositions express a connection. E. g. : As 
the life so is the death. 

Their truth depends on the correctness of the connection. 

(6) . idversative, or discretive, propositions include several 
different judgments separated by some such particle as but, yet, 
nevertheless, etc. E. g. : Not on riches, but on virtue, depend" 
happiness. 

The truth of these propositions depends on the truth of their 
parts and of the opposition between them. 

II. Four types of apparently simple, but really complex, propo- 
sitions. 

(1) Exclusive propositions which assert that an attribute be- 
longs to but one subject, as: God alone is to be loved for Himself. 

(2) Exceptive propositions affirm an attribute of a subject, 
but with the exception of some subdivisions of that subject. 
E. g. : Excess is possible in all the virtues except in the love of 

Cod. 

(3) Comparative propositions say not only that a thing is so, 
but that it is more so or less so than some other thing. E. g. : 
Wisdom is more valuable than fortune. 

(3) Inceptive, or desitive, propositions assert that a thing has 
commenced or ceased to be so. E. g. : The independence of Bel- 
gium dates from 1830. 

Each of these four propositions really includes two judgments ; 
it is not true unless the two parts are true. 



84 LOGIC 



§ 3. Relations Betzveen Propositions 

40. Relations Between Propositions. — Various kinds of rela- 
tions between propositions are to be distinguished : their equiva- 
lence, convertibility, subordination, opposition. 

41. Equivalence of Several Propositions. — Propositions are 
called equivalent when they differ only in expression, and in 
reality are identical as to sense and logical value. E. g. : Every 
man is just; there is no man who is not just. 

42. Convertibility of Propositions. — Conversion consists in 
transposing the two terms of a proposition so that the new 
propositions so obtained shall also be true if the original is true. 

(1) The universal negative is convertible, for both the terms 
are universal. E. g. : No mineral is capable of vital functions ; 
no being capable of vital functions is a mineral. 

(2) The particular affirmative proposition is convertible, for 
here, also, the two terms are of the same extension. E. g. : Some 
sentient beings are endowed with reason; some beings endowed 
with reason are sentient. 

In these two cases the convertibility is evident: the two terms 
are purely and simply interchangeable. 

These are in fact the only cases of interchangeability. 

(3) It must be noted, first of all, that singular propositions 
.are never susceptible of any but an apparent conversion, since 
.a determinate individual term, representing in the last analysis 
a first substance, cannot serve to express a formal predicable 
idea. E. g., whether I say, "Peter is a learned man," or, "A 
learned man is Peter," the same Peter, in spite of the inversion, 
will still be the subject. 

(4) The universal affirmative is susceptible of conversion, in 
the sense that the predicate can take the place of the subject and 
vice versa, but on condition that the subject turned into a predi- 
cate is modified by some mark of particularity with a restrictive 
sense. The conversion effected on these conditions is said to be 
imperfect. E. g. : All men are sentient ; certain beings endowed 
with feeling are men. 

There must still be an exception in the essential definition, 
where the idea defined is equal to the definition. 



FORMAL ( U SK OF LOGICAL ORDER 35 

This "imperfect" conversion is no true conversion, for this 
consists in the simple mutual substitution of the two terms. 
The addition of a sign of particularity which renders the conver- 
sion imperfect alters its nature. 

43. Relations of Opposition and Subordination. — These rela- 
tions between propositions may be produced in four different 
ways : propositions are contradictory, contrary, sub-contrary, or 
subaltern. The first two are relations of opposition properly so 
called. 

(1) Judgments so opposed to each other as to exclude any 
intermediate judgment are said to be contradictory. They differ 
both in form and in quantity. E. g. : Every man is white ; some 
man is not white. 1 

(2) Judgments which differ only in form, and have the same 
universal quantity, are so opposed to each other as not to exclude 
any intermediate judgment, and are called contraries. E. g., 
every man is just; no man is just — two extremes between which 
a third judgment may be slipped in: Some man is not just. 

(3) Propositions which differ only in form, and have the 
same particular quantity, are sub-contrary. E. g. : Some man is 
just; some man is not just. 

(4) Propositions which have the same form, and differ only 
in quantity, are subaltern. E.g.: Every man is just; some man 
is just. — No man is just; some man is not just. 

Logicians have adopted the convention of designating by the 
letters A, E, I, O, the four kinds of propositions as distinguished 
by quantity and form. 

A designates a universal affirmative proposition. 

E designates a universal negative proposition. 

I designates a particular affirmative proposition. 

O designates a particular negative proposition. 

The following scheme exhibits the contradictory and contrary 
modes of opposition. 2 



1 Perili erm., c. VI. 

2 "A universal affirmative (proposition) and a universal negative 
are contrary, as Every man is just, No man is just: for a universal nega- 
tion indeed not only does away with a universal affirmation, but also in- 
dicates the extreme distance, inasmuch as it denies all that the affirmative 
asserts: this is of the essence of contrariety, and therefore the particular 



3C 



LOGIC 



o 



Every man 


is 


CONTRADICTORIES 


One man is not 


just 






just 


I 

One man is 


just 


CONTRADICTORIES 


E 
No man is just. 



44. Rules on the Truth or Falsity of Opposed Propositions. 

— (1) Contradictories are never either both true or both false, 
seeing that one is the negation pure and simple of the other. 
The truth of the one, then, carries with it the falsity of the other; 
and vice versa, the falsity of the one implies the truth of the 
other: If it is true that every man is just, it cannot be true that 
one man is not just. 

(2) Contraries cannot both be true, but they can both be false.. 

Contraries cannot both be true ; otherwise contradictories- 
would be true at the same time. Suppose the proposition, "Every 
man is just," to be true ; the contradictory, "One man is not just,"' 
is false. If it is false to say that one man — even a single indi- 
vidual — is not just, much more is it false to say that every man 
is not just, or — which comes to the same thing — that no man is 
just. The proposition, "No man is just," is the contrary of the 
proposition, "Every man is just." 

But the falsity of a proposition does not imply the truth of the 
contrary. It may be false that all men are just without its being 
true that no man is just; there may be some just men, even 
though not all are just. 

(3) By a rule opposed to that of contraries, sub-contraries 
may both be true. E.g.: Some man is just; some man is not 
just. Justice may be an attribute of one portion of mankind and 
not of the other. 

But sub-contradictories cannot both be false, or both of two- 
contradictories would be false. Let the proposition, "Some man 
is just," be false; the contradictory, "No man is just," is there- 



affirmative and the particular negative are in the nature of a mean be- 
tween the contraries. ... In contradictories the negation does no- 
more than remove the affirmative." St. Thomas, In Periherm., Lect. XI. 



FORMAL CAUSE OP LOGK KL OR »ER 37 

fore true. .Much more, then, is it true that some man is not just, 
which is the sub-contrary. 

45. Rules Concerning- the Truth or Falsity of Subaltern 
Propositions. The particular propositions I, O, are subordinate 
to universals A, E, respectively. 

The truth of universal propositions implies that of their sub- 
alterns; Inn the truth of subalterns di es hot carry with it that of 
their universals. 

The falsity of particulars implies the falsity of universals; but 
the falsity of universals duos not carry with it the falsity of 
part iculars. ' 

46. Immediate Inferences. — We shall presently sec that, in a 
reasoning properly so called, the conclusion springs from the 
comparison of three different terms, and that this comparison is 
made in two propositions, the two premises of the reasoning. 
It is sometimes permissible to draw at once a sort of conclusion 
from the enunciation of a single proposition: this is called an 
immediate inference. 

The conversion, opposition, and subordination of propositions 
give 1 ccasion to inferences of this kind. 

The rules given above sufficiently show how these inferences 
are justified. 

ARTICLE IT. 
Reason i \<; 

47. Preliminary Remarks. Object of Article II. — Chapter III 
of this treatise has for its object the formation <>i the logical 
order. 



1 With regard to modal propositions, the contradiction betwee' 1 
affirmation and negation does not fall upon the attribute of the proposi- 
tion, hut upon the verb. The most ordinary ca^es of opposition between 
modal propositions arc set forth in the following scheme: 

This must he so. CONTRADICTORIES This 1Uc( ' n,,t ' )C s o — 

q It is possible that this 

■V/>, is not so. 
It is not impossible 'o'//. 
that this is so — This s 

may be so. CONTRADICTORIES This cannot be so. 



38 LOGIC 

In a former article we saw how concepts perform their func- 
tions in a judgment, and terms in a proposition. We next classi- 
fied judgments, then set them side by side and compared them. 

Judgments in their turn form the elements of a more complex 
order. Known judgments lead to a new judgment, through a 
discursive process called reasoning. This process, when expressed 
in words or writing, is called syllogism. 

Hence these two paragraphs : 

Reasoning and syllogism (§1). 

The various forms of these two (§ 2). 

§ 1. Reasoning and syllogism 

48. Reasoning. — The aim of all intellectual processes is the 
knowledge of truth. 

Certain truths are known immediately ; others, mediately, by 
means of those known immediately. The former, as generating 
the latter, are called principles; the latter are consequences, or 
conclusions. To proceed from principles to conclusions is to 
reason. 

A conclusion is a proposition, and, as such asserts a predicate 
of a subject. When the predicate manifestly' belongs to the sub- 
ject, the proposition is evident. 1 This evidence is immediate 
when the objective connection between the predicate and the 
subject of a judgment is immediately apparent to the intelli- 
gence ; also immediate is the corresponding certitude. But in 
most cases the evidence of the judgment is brought to light only 
by the employment of one or more intermediaries, or middle 
terms — common terms of comparison between subject and predi- 
cate. In such cases the evidence is mediate, or by reasoning. 
as is the corresponding certitude. The kind of evidence is the 
evidence proper to conclusions. 

The necessity of this discursive proceeding arises from the 
disproportion between the complexity of intelligible things and 
the inadequacy of the intelligence which is called upon to know 
them. 2 



1 See Criteriology. 

2 "The discourse of reason always begins in the understanding and 
ends in the thing understood ; for we reason by proceeding from certain 



F( IRMAL C U'SH i >F l.( >GIC \l. I IRDJ R 39 

The power of reasoning urges a perfection which the 
metaphysicians call mixed, i. e., marked by imperfection. 

h is a perfection to be able to reason, i. e., to reach the knowl- 
edge of truths which otherwise would remain unknown. 

It is an imperfection to be obliged to reason, i. e., to reach the 
truth only by winding and difficult paths. 

49. The Syllogism. Terminology. — Reasoning, then, con- 
sists in comparing the subject and predicate of a not evident 
judgment, which is to be the conclusion, with a middle term to 
see whether, objectively, the one implies the other or excludes it. 
Its complete and typical expression is the syllogism. "The syllog- 
ism", says Aristotle, "is a discourse in which, certain thing; 
being laid down, another thing follows necessarily, simply be- 
cause those things are laid down." 1 

When the reasoning faculty declares that the predicate 
agrees objectively with the subject, the conclusion is affirmative; 
when it sees that one of the two terms agrees with the middle 
term while the other does not, the conclusion is negative. 

The two terms of the conclusion are called extreme terms, or 
extremes, in opposition to the middle term (mcdiits terminus) 
with which they are both compared. 

The predicate is called the great extreme; the subject, the 
small extreme. 

The two propositions from which the conclusion is drawn are 
called premises 1 prcemittuntur conchisioni) ; together they form 
the antecedent. The premises are those things which, according 
to Aristotle, once laid down or supposed, draw the conclusion 
after them. 

The consequent is the conclusion. The proposition first in 
order to be enunciated is often called the major; the second, the 
minor. But more exactly, the proposition in which the great 
extreme is put with the middle term is called the major (Major, 
propositio) ; that in which the small extreme is compared with 
the middle term, the minor (Minor, assumpta). 



understood things; and the discourse of reason is complete when we 
arrive at the understanding of what was previously unknown. Our 
reasoning, therefore, proceeds from some precedent understanding." 
Summa Theol., 2 a 2*, q. 8, a. 1, ad 2. 
1 Prior Anal, I. 1. 



40 LOGIC 

The premises and the conclusion, the antecedent and the con- 
sequent, constitute the matter of the syllogism. The form lies in 
the bond between the antecedent and the consequent ; it is con- 
densed in the particle therefore, which expresses the consequence 
(consequcntia, consecutio) of the syllogism. 

To study the nature of reasoning is to investigate what 
causes that "certain things being laid down, another thing must 
necessarily follow simply because those things are laid down." 

50. Nature and Logical Basis of the Syllogism. — Take for 
example this syllogism : The triangle which has two equal sides 
has two equal angles. This triangle has two equal sides. There- 
fore it has two equal angles. 

To reason is to place within the extension of an abstract type 
some ■determinate subject, with the result of concluding thai a 
note which belongs to the abstract type as such is attributable to 
this determinate subject. 

The major is a necessary proposition: it asserts that -the pred- 
icate of the conclusion (the property of having two equal angles) 
is necessarily associated with an abstract middle term (a triangle 
which has two equal sides). 

Being abstract, this middle term is not actually universal, but it 
can be universalized; by an ulterior act of reflection it can be at- 
tributed to one, or to several, or to all the inferiors of a species 
or of a genus. 

The reasoning faculty, on enunciating the minor, sees that the 
middle term extends to the subject of the minor — it sees that this 
triangle has two equal sides. 

Then, provided that the major and the minor. are taken in at 
one glance, it will be seen that the predicate of the conclusion has 
two angles equal, necessarily belonging to the middle term, tri- 
angle with two sides equal, belongs to the subject of the conclu- 
sion which is within the extension of the middle term ; therefore 
the necessary connection between the subject of the conclusion and 
its predicate becomes obvious. 

The syllogism is essentially a process of univcrsalization. The 

principle on which it is founded may be thus enunciated : The note 

which necessarily applies to an abstract subject — the middle term 

■ — applies to the subjects of the extension of the middle term. 

' Obviously, the connection established bv reasoning; between 



!•'< >KM \l. CAUSE < >T L( )GIC \L ( >RDER | I 

tin- extremes and the middle term belongs at once t" the compre- 
hension and to tin- extension of the terms. 

In the major, one of the extremes— the predicate of the con 
sion — is, by reference to its comprehension, connected with the 
middle term: Whatever things arc the same as a third thing arc 
the same as one another. 

In the minor, the same middle term is considered with refer- 
ence to it- extension and in this point of view is connected widi 
the other extreme, the subject of die conclusion. Whatever is 
affirmed or denied of a subject taken in the abstract must he 
affirmed or denied of <'// its inferiors and each one of them, in one 
word, affirmed or denied universally. 

The syllogism considered above lead- to an affirmative conclu- 
sion. The same analyses may be applied to syllogisms with nega- 
tive ci inclusions. 1 

51. What Kind of Necessity Attaches to the Principles of the 
Syllogism? — The law which serves as a fulcrum for reasoning 
is sometime- metaphysical, or absolute (see example given under 
50) ; sometimes physical, or natural, and therefore dependent on 
conditions to be determined by experience (as: Water attain- it- 
maximum density at 4° centigrade). 

Tn the former case the predicate in the conclusion expresses 
the essence, total or partial, of the middle term, or a property 
which is a corollary of that essence, and the necessity of applying 
this 'predicate to the subject of the conclusion is absolute. 

In the latter case the quality is attributed to the middle term in 

virtue of a law established by experience, and the attribution of 

predicate to subject in the conclusion is hypothetic ally necessary. 

These law- of experience are established by induction, as will be 

later. 

52. Logical First Principles. — We have seen that the syllogism 
derives its demonstrative force from a necessary proposition. 
Whence does this proposition derive it- logical value? From a 
previous reasoning. We cannot go on from one process of rea- 
soning to another indefinitely. 2 



i Sec ( riteriology, n°. 58: Stuart Mill'- objections against the value 
of the syllogism. 
- Criteriology, 52-54. 



42 LOGIC 

Otherwise we should be obliged to say that no -conclusion is cer- 
tain. There must be propositions on which the reasonings are 
supported, and which themselves need no demonstration. These 
are called logical principles: they are the enunciation of a relation* 
between primary notions. 

There are two kinds of principles : (1) generative principles of 
the sciences; (2) directive principles, or axioms. 

53. Figures and Modes of the Syllogism. — The various forms- 
of the syllogism, according to the relation of the middle term 
with the extremes, are called by Aristotle -figures (o-xyv-*™)'- 

1st Figure: The middle term is subject in the major and attri- 
bute in the minor. 

2nd Figure : The middle term is attribute in both premises. 

3d Figure: The middle term is subject in both premises. 

The syllogisms possible in these figures, regard being had to* 
the quantity (universal or particular) of the propositions and their 
form (affirmative or negative) have been called the modes of the 
syllogism. 

Counting all the possible modes of the syllogism, independently 
of their logical value, we find a total of 256 forms. Of these 21 
are conclusive ; and 5 of these 24 are useless without being vicious. 
Hence we have 19 valid and useful modes of the syllogism. 

54. Rules of the Syllogism.— Besides the special rules of each 
of the figures, logicians have been wont to formulate eight rules 
applicable to the syllogism in general, expressing the nature of the 
reasoning. 

First Rule. — Terminus esto triplex: medius, major que mi- 
norque. — The syllogism must have three terms, neither more nor 
fewer. To reason is in fact to compare two terms with one and 
the same third, so as to see what logical relation exists between 
the two terms so compared. 

This rule may be violated by defect, in using only two terms, or 
by excess, in using more than three. 

(1) A syllogism with tzuo terms is, e. g., where one of the 
premises is tautological. E. g. : Every effect has a cause. But 
the universe is an effect. Therefore the universe has a cause. 

This first rule is violated by the form of sophism called petitio- 
principii, which resolves the question by the question (begging the 
question). 



i i IRM \1 I \i si. "I I I iGK \l. < IRD] \< 13 

(2) A syllogism contains more than three terms when one 
term is equivocal and is taken in different acceptation-. E.g.,: 
The operations of thought have the brain as organ. An opera- 
tion which has the brain as organ is material. Therefore the 
operations of thought are material. 

In this syllogism the middle term, has the brain as organ, is 
equivocal. 

Second Rule. — Latins hoc (terminus extremes) quam prce- 
missce conclusio non vnlt, or: AZquc ac pneinissa? extendat con- 
clusio voces. — The extremes must be the same in the conclusion 
as in the premises. 

The conclusion expresses the results of the comparison made 
in the premises. It cannot go beyond that ; otherwise it would 
pass from the terms compared in the premises to other terms,. 
and thus would violate the first rule, the essential condition of 
reasoning. 

Third Rule. — Ant semel out iterum medius generaliter esto. 
• — The middle term must be taken as universal in one premise at 
least. 

The analysis of the process of reasoning (50) has made 
this third rule intelligible. If the middle term were taken twice 
in a restricted sense, that part of its extension which it represents 
might possibly be different in the two cases, and there would be 
four terms in the syllogism (first rule). E.g.: Every metal 
is heavy. This substance is heavy. Therefore this substance is a 
metal. The middle term, heavy, is not universal in either of the 
premises. 

This very common sophism is characterized by the adage : Ab 
uno disce omnes. 

Fourth Rule. — Nequaquam medium capiat conclusio fas est. 
— The middle term may not enter into the conclusion. 

It is for the conclusion to apply to the two extremes the result 
of the comparison made in the premises between them and the 
middle term. To introduce the middle term into the conclusion, 
then, would be to miss the aim of the reasoning. 

Fifth Rule. — Amine afh'rmantes nequeunl generate negatem. 
— Two affirmative premises cannot beget a negative conclusion. 

If two ideas agree with one and the same third idea, the other 
rules of the syllogism being observed, they cannot but agree with' 



44 LOGIC 

each other ; and the identity affirmed in the premises cannot be 
denied in the conclusion. . 

Sixth Rule. — Utraquc si prcemissa neget, nil inde sequetur. — 
With two negative premises no conclusion is possible. 

Two extremes both excluded from one middle term cannot 
t>e connected with each other on account of this exclusion. 

But on the other hand, it is possible that two terms excluded 
from one given middle term may be comparable with another 
middle term with which both must be coupled, or else one coupled 
and the other separated. The use of this other middle term would 
.give a conclusion. 

The fact, then, that two extremes are excluded from a given 
middle term warrants no assertion as to the relation of the ex- 
tremes. 

Seventh Rule. — Pejorem sequitur semper conclusio partem. 
— The conclusion should follow the premise of lower rank. 

This formula has a double application : 

(1) // one of the premises is negative, the conclusion must be 
negative. If, of two ideas A and B, A agrees with a third idea, 
C, while B does not, it is impossible to conclude therefrom that 
A agrees with B. 

(2) // one of the premises is particular, the conclusion cannot 
be universal. 

As the premises cannot both be negative (sixth rule), only two 
•cases are to be considered : 

(a) Both the premises are affirmative. 

(b) One is affirmative; the other, negative. 

In case (a) both the predicates are particular; one of the two 
subjects is by hypothesis particular: there is, then, only one 
universal term in the premises. As this must be the middle term 
(third rule), neither of the extremes is universal in the premises 
and, consequently, cannot be so in the conclusion. So that the 
conclusion, since it necessarily has a particular subject, is par- 
ticular. 

In case (b) the premises include two universal terms: the 
predicate of the negative premise and the subject of the proposi- 
tion which, by hypothesis, is universal. 

But the conclusion is negative, so that its predicate is universal. 
This term, which is the predicate in the conclusion, is not the 



F( IRMAL C UJSE I IF LOGICAL I >RDER 1-5 

middle term (fourth rule). The second universal term of the 
premises is therefore the middle term. Hence the extreme which 
becomes the subject of the conclusion is particular in the premises, 
and, consequently, in the conclusion. Therefore the conclusion 
is particular. 

For example : Every man is corporeal. But A is not cor- 
poreal. Therefore A is not a man. 

The result would he the same if one proposition were both uni- 
versal and negative, as: No man is spiritual. But A is a man. 
Therefore A is not spiritual. — Or: But B is spiritual. Therefore 
B is not a man. 

When one premise is particular, then, the conclusion must be 
particular. 

Eighth Rule. — Xi! sequitur (/(■minis ex particularibus 
iinqitani. — -No conclusion follows from two particular premises. 

As both the premises cannot be negative (sixth rule), the only 
possible cases are : 

(a) Both premises are affirmative. 

(b) One is affirmative; the other, negative. 

In case (a) all the terms are particular: the two predicates, 
because the propositions are affirmative; the two subjects, by 
hypothesis. The middle term, therefore, is not once taken uni- 
versally. The third rule is violated. Xo conclusion. 

Example: Some men are rich. Some men are ignorant. 
Therefore some rich men are ignorant. 

If this syllogism were valid, it might he proved in the -aim- 
way that some rich men are poor, which exposes the sophism. 

In case (b) the premises contain only one universal term, the 
predicate of the negative premiss. But the conclusion being neg- 
ative, its predicate is universal; being so in the conclusion, it must 
also be universal in the premises. Consequently, the middle term, 
which cannot he identical with the predicate of the conclusion 
(fourth rule), is twice particular in the premises. ( )nce more, 
the third rule is violated. No conclusion. 

Example : Some men are learned. But some men are not 
virtuous. Therefore some learned men arc not virtuous. 

The inconsequence is manifest. 

55. Range of the Rules of the Syllogism. Logic and Truth. 
— The rules just given relate only to logical deduction. But 



46 LOGIC 

logical connection between antecedent and consequent is one 
thing; the truth of the consequent is another. The necessary 
connection between the things laid down and the thing which 
springs from them does not affect the truth or falsity of the 
premises containing the former. 

Two general laws govern the truth and the falsity of conclu- 
sions : 

(1) If the premises are true, so will be the conclusion: ,Ex 
vero non sequitur nisi verum. The conclusion, indeed, confines 
itself to affirming relations seen in the premises ; if they have 
been recognized in the premises, there can be no error in ex- 
pressing them in the conclusion. 

Corollary: As true premises cannot lead to a false conclu- 
sion, we may fairly refute a doctrine or a theory by arguing from 
the falsity of its consequences. Atheism, for example, is refuted 
by its consequences. 

(2) If the premises are false, or if one of them is 'false, the 
conclusion will generally be false; but it may be true. Ex falso 
sequitur quidlibet. 

Examples given by Aristotle : "Every man is a mineral. Every 
mineral is an animal. Therefore every man is an animal." — 
"Every mineral is an animal. No horse is an animal. Therefore 
no horse is a mineral." — "Every horse is an animal. N'o man is 
an animal. Therefore no man is a horse." 

From a false principle one may arrive at an exact result, either 
because the principle is a mixture of true and false, and it has 
been used only in so far as it is true; or because the errors pro- 
ceeding from the principle have ended by compensating one an- 
other. 

Corollary: Since a false antecedent may have a true conse- 
quent, a doctrine or theory cannot be rigorously established by 
showing that this or that one of its consequences is true. Newton, 
for example, had deduced from his theory of emissions many 
consequences in respect to the nature of light which were after- 
wards verified by experiment ; nevertheless, the theory itself was 
disproved. For an argument drawn from the consequences of a 
theory to be conclusive, it must be demonstrable that the theory 
leads to none but true consequences. 



FORMAL I A.USE OF LOGICAL ORDER 17 

§ 2. Syllogisms 

56. Preliminary remarks. — Syllogisms may be classified either 
by their form or by their matter. The form of a syllogism is its 
structure, abstracting from the truth or falsity of the premises 
themselves; the matter consists of the propositions, which may 
be true or false. 

In the following two articles we shall successively take the two 
points of view of form and of truth. 

Scientific induction does not essentially differ from the syl- 
logism. Hence the analogy and the example, which logicians 
connect with induction, may also be reduced to the syllogistic 
process. It follows that all forms of reasoning properly so 
called are but variants of the syllogism. Such will be the gen- 
eral conclusion to be drawn from this article. 

I. Syllogisms Considered with Reference to Their Form 

57. Classification of Syllogisms by Form. — Considered with 
reference to its form, the syllogism is : categorical; hypothetical 
(or conditional) ; conjunctive ; disjunctive. The latter two may 
be reduced to the hypothetical syllogism. The exclusive syllog- 
ism and the dilemma, which are complex, more properly belong, 
the former to the categorical type, the latter to the hypothetical. 

58. Varieties of the Categorical Syllogism. — The categorical 
syllogism has for its premises two categorical propositions. It 
will be useful to note some of its possible structural modifica- 
tions. 

Such are the forms of reasoning called epicheireme, poly- 
syllogism and sorites, enthymeme. 

(1) The epicheireme (erl and x «/»<2 , to take in hand) 
now 1 designates a syllogism one or both premises of which is 
immediately accompanied by the proof. 

The poly syllogism is a series of syllogisms in which the con- 
clusion of each serves as premise for the next. 

In practice the polysyllogism is condensed, under the form of 



1 In Aristotle epicheireme means an attempt at demonstration as 
opposed to a demonstration properly so called. 



48 LOGIC 

sorites (cQpos, heap), into a series of propositions where the 
predicate of the first becomes the subject of the second, and so 
on, in such a way that the predicate of the last in the series may 
be coupled with the first subject. 

Example : The human soul forms abstract thoughts ; a being 
capable of abstract thoughts is spiritual ; a spiritual being is by 
nature imperishable ; a being naturally imperishable cannot be 
annihilated ; a spiritual being that cannot be annihilated will live 
with an immortal life; therefore the human soul is immortal. 1 

59. Nature and Rules of the Conditional Syllogism. — The 
conditional syllogism is that which has a conditional proposition 
for its major. E.g.: If the soul is simple, it is imperishable;. 
but the human soul is simple ; therefore it is imperishable. 

In the major there is only the assertion of a necessary connec- 
tion between the condition (simplicity of the soul) and the con- 
ditioned (incorruptibility). 

As soon as this connection is accepted as necessajy, the rest 
reduces to an ordinary reasoning the antecedent of which forms 
the minor and the consequent conclusion. 

The whole interest of the conditional syllogism, then, is in the 
major, which is equivalent to an absolute affirmative proposition. 
The proposition, "If the soul is simple, it is imperishable," is 
equivalent to, "Every simple thing is imperishable." Now a uni- 
versal affirmative is not convertible (42). 

From this observation we deduce the rules of the conditional 
syllogism : 

(1) Affirm the condition, or antecedent, and you must affirm 
the conditioned proposition, or consequent. E. g. : If you are from 
Brussels, you are a Belgian. But you are from Brussels. There- 
fore you are a Belgian. 

(2) Deny the conditioned proposition, or consequent, and you 
must deny the condition, or antecedent. E. g. : If you are from 



1 The enthymem* is commonly reckoned among the more or less 
disguised forms of the syllogism, as though it consisted merely in leaving 
one of the premises to be understood, not expressed. This is too sec- 
ondary a circumstance to justify giving the enthymeme a place of its own 
among the forms of syllogism. As a matter of fact Aristotle understood 
by enthymcvie a syllogism the conclusion of which is only more or less 
probable. 



I I IRMAL CAUSE I »!•' LOGICAL I >RDER 49 

Brussels, you are a Belgian. But you arc not a Belgian. There- 
fore you are not from Brussels. 

But the inverse is not true. 

Remarks: (1) Nevertheless, the matter of the conditional 
proposition may possibly be such that the truth of the consequent 
carries with it the truth of the antecedent. E. g. : If a figure is a 
circle, it has equal radii. 

i .' ) The conjunction if does not always mean, in the thought 
of one who uses it, a connection of necessary dependence between 
the antecedent and the consequent ; it frequently indicates only a 
partial or a contingent connection, and in that case expresses a 
presumption rather than a rigorous inference. E. g. : If this man 
were sorely tried by misfortune, he would return to a better state 
of mind. 

60. Conjunctive and Disjunctive Syllogisms. — The conjunc- 
tive syllogism is that which has a conjunctive proposition for its 
major. This proposition alleges an incompatibility between two 
cases, one of which is affirmed in order to eliminate the other. 

E. g. : You could not have been in Brussels and in Paris at the 
same time. You were in Brussels. Therefore you could not have 
been in Paris. — This syllogism may be reduced to the conditional 
type, and follows the laws of that type. 

The disjunctive syllogism has for its major a disjunctive prop- 
osition, which not merely alleges an incompatibility, but implies 
an alternative admitting no middle term. 

Hence the disjunctive syllogism is governed by the following 
two rules : 

(1) The disjunction laid down in the major must be complete. 

i 2 i When the minor affirms one of the members of the dis- 
junction, the remaining member or members must be denied in 
the conclusion, and vice versa. 

Example : Every free act is morally good or bad. Now such or 
such an act (e.g., an oath) is not morally bad; therefore it is 
morally good. . . . Or. it is bad ; therefore it is not good. 
. . . Or, it is good ; therefore it is not bad. . . . Or, 
it is not good ; therefore it is bad. 

61. Exclusive Syllogism. — This type has both premises exclu- 
sive. E. g. : Only a spiritual being is free. Man alone is spiritual. 
Therefore he alone is free. 



50 LCGIC 

This syllogism may be broken up into two others, one affirma- 
tive, the other negative : A spiritual being is free. Man is spirit- 
ual. Therefore he is free. — A free being is spiritual. Beings 
other than man are not spiritual. Therefore they are not free. 

62. Dilemma. — The dilemma is the combination of a disjunc- 
tive proposition, serving as major, with two or more conditional 
propositions forming a minor. First, partial conclusions exclude 
the members of the disjunction one after another; then it is' con- 
cluded in a general manner that the disjunctive proposition taken 
as a whole is inadmissible. 

This method of arguing is lively and cogent. An alternative is 
presented to one's opponent : he is left the choice between two 
positions ; then it is proved that in either case he is wrong. 

The validity of the dilemma requires a punctual observance of 
the rules of the disjunctive and of the conditional syllogisms. 

First rule: The disjunction of the major admits of no inter- 
mediary proposition, but must be complete. 

Second rule: Each of the two conditional syllogisms which 
together form the minor of the dilemma must be conclusive, and 
must lead to the same conclusion. 

Example (from Pere Felix) : "If we supposed that Jesus 
Christ, in spite of His own assertions, is not God, we should 
be led to one of these two insulting conclusions : that He is a 
madman ; or that He is an impostor. Now, supposing Jesus 
Christ to be insane, how can we reconcile with insanity the lofty 
wisdom manifested in His life and doctrine? Supposing Him 
an impostor, how make His humility and abnegation agree with 
such ambitious designs? Both these hypotheses, therefore, are 
equally inadmissible : Jesus Christ is the Christ, the Son of the 
living God." 1 

It is easy to show that the syllogisms are fundamentally re- 
ducible to the categorical syllogism. 



1 The dilemma must not be confounded with reasoning "by suc- 
cessive parts", which consists in enumerating all the species of a genus, 
to take them up afterwards one by one and finally enunciate of all the 
conclusion which is valid for each of the parts. 



FORMAL CAUSE < >F L< »G1( \l. ( IRDER 51 

II. Syllogisms Considered with Reference ro T] 

Matter. 

63. Preliminary Remarks. — Syllogisms arc divided, in respect 
to their matter, according to the relations of their propositions 
with the truth. Now, judgments are certain, probable, or 
erroneous; and syllogisms, accordingly, are demonstrative, prob- 

erroneous. 

I 1 i The judgment is certain when the mind firmly adheres to 
what it knows to be the truth: a syllogism which leads to certi- 
tude is a demonstration. 

I 2 I So long as the mind remains between two opposite judg- 
ment- without definitely adhering to either of the two, it is in 
suspense, — it doubts. When it inclines to one side or the other, 
but without adopting either side absolutely to the exclusion of 
the other, it has an opinion: the syllogism is probable when it 
begets an opinion, and its probability is in the direct ratio of the 
strength of the motives which induce the partial adherence of 
the mind. 

: 3 i The contrary of truth, the disagreement of the judgments 
with the thing known, is error: syllogisms which lead to error 
are called sophistical. 

We proceed to examine in order demonstrations, probable 
arguments, and those sophisms which are chiefly worthy of our 
attention. 

Different Kinds of Demonstration. 

64. I. Primary Division. — A demonstration is a reasoning 
which proceeds logically from certain premises to a certain con- 
clusion. And in a more perfect >ense, it is a syllogism which fur- 
thermore produces true knowledge, i. e., makes us "know the 
cause of the thing, know that that cause is really the cause of 
the thing, and that, consequently, the thing could not be other- 
wise than we know it." 1 

There is a primary distinction between the demonstration which 



i Aristotle. Posterior Anal.. I, :.'. 



52 LOGIC 

produces a certain conclusion and that which produces a strictly 
scientific conclusion. 

65. Conditions of a Strictly Scientific Conclusion.— Examin- 
ing into the nature of the scientific demonstration, Aristotle de- 
termines its properties as follows : 

The premises of the determinate syllogism must be true, pri- 
mary, immediate, better knotwi than the conclusion, anterior to it, 
and the cause or reason of its truth. 

(1) True: Although false premises may sometimes be followed by 
a true conclusion (57), falsity as such is never the origin of a 
truth. The aim of the demonstration being to bring a true con- 
clusion out of the premises, a good demonstration must proceed 
from true premises, the natural source of truth. 

(2) Primary — themselves incapable of demonstration — in the 
sense that all the demonstrations of a science should form a 
single chain, the first link of which is formed out of premises 
that cannot be demonstrated. Hence, in relation to those which 
follow them, these primary premises are : 

(3) Immediate, i. e., evident without need of demonstration. 

(4) The cause or reason 1 of the conclusion, not only in the 
logical order of our knowledge, but in the ontological order. 

(5) Anterior to the conclusion, since the premises must con- 
tain the cause or reason of the conclusion. This anteriority may 
be only a priority of nature. 

(6) Better knozvn than the conclusion, the aim of reasoning 
being to effect a passage from what is better known to what is 
less, or not at all, known. Observe that this Aristotelean theory 
refers to the ontological order. In our subjective point of view 
the sensible fact precedes the abstract quiddity which we 
separate from it ; the particular leads to the universal. But in 
reality nature is prior to its sensible manifestations, the law is 
the reason why the fact is, and is necessary to its explanation. 

66. Proof of Fact and Causal Demonstration. — Correspond- 
ing to the fundamental distinction between the syllogism with a 
certain conclusion and the strictly scientific demonstration is the 
Aristotelean division of the proof of fact and the causal demon- 
stration. 



1 On this distinction see General Metaphysics, n°. 165. 



n IRM \l I MM- ( IF L( >GIC \l. I IRDER 

The demonstration Srt, demonstratio quia, or quod (quia 
meaning not because, but that), is ///r proof that something t'j. 
\>- >rding to Cajetan, this proof bears both on the copulative 
md upon the existence, especially on the latter. 3 

The causal demonstration Si6ti, demons/ratio propter quid, 
brings into evidence the immediate anise of the thing demon- 
strated, the proper reason, &px*t oUeia, for which it is. Thi 
why it is strictly scientific. 

\ demonstration which gives an extrinsic or a general reason 
for the connection of the predicate with the subject is not a 
demonstration 8i6n. but is ranked among proofs of fact. 

67. II. Demonstrations a Priori, a Posteriori. — This distinc- 
tion, which, with modern logicians, takes the place of the preced- 
ing, is less rigorous, hut has a foundation in the nature of things. 

A demonstration is a priori or a posteriori accordingly as the 
middle term is in reality anterior or posterior to the predicate of 
the conclusion ; it proceeds from the cause or the reason (a causa 
vel ratioite quae in se est prior — a priori) to the effect or result 
( (/</ effeetum vel rationatum) , or vice versa. — E. g. : An imma- 
terial subject is imperishable. The human soul is immaterial. 
Therefore it is imperishable. — A being which is subject to change 
requires a cause other than itself to bring about its existence. 
1"he universe is subject to change. Therefore there is a cause of 
the existence of the universe, God. 

To this division some authors have added a third member, the 
demonstration a simultaneo or quasi a priori. It has its place 
where two things have to be demonstrated which in reality are 
not distinct, but one of which is necessarily conceived as coming 
before the other. Such is the proof by which St. Anselm thought 
it possible to demonstrate the existence of God from the idea of 
the most perfect Being. 

68. III. Circular or Retrogressive Demonstration. — The rea- 
soning faculty ascends from effect to cause that it may descend 
again from cause to effect and account for the latter by the former. 
It describes as it were a circle, returning, in a manner, to the 
point from which it started. This process is called circular de- 
monstration. 



i Posterior Anal. [I, 1. 



54 LOGIC 

The circular demonstration sets out from a -phenomenon the 
existence of which is established, but its nature only confusedly 
perceived; it starts again from the nature of the phenomenon, 
but only after acquiring a more distinct idea of it, which better 
explains observed effects. 

The circular demonstration must not be confounded with the 
vicious circle. 

69. IV. Other Accidental Forms of Demonstration.— -d ) 
Direct and indirect demonstration: This distinction is connected 
rather with extrinsic circumstances than with the nature of 
things. The direct demonstration (including all the forms thus 
far enumerated) shows, without any deviation, that the con- 
clusion is virtually contained in the premises. The indirect de- 
monstration, taking into account the subjective dispositions of 
the person to whom it is addressed, demands his positive ad- 
hesion to the truth of the conclusion through the rejection of the 
contradictory proposition. E. g. : The demonstration of free will 
by proving the absurdity of the consequences of determinism. 

The indirect demonstration is also called demonstration by the 
impossible, or reductio ad absurdum. 

(2) Absolute and relative, or ad homincm, demonstration. 

(3) Aristotle also opposes to the scientific demonstration a 
demonstratio a signo or per signum, an extrinsic proof adduced 
from things exterior to that which is to be demonstrated. See 
example ( 74 ) . 

These accidental or secondary forms of demonstration may be 
reduced to the fundamental distinction between trie demonstration 
on, and 5l6tl. 

Probable Arguments. 

70. Probable Arguments. — They are those arguments which 
proceed from one or more probable premises to a conclusion 
which is only probable. 

Under one heading may be classed the various arguments 
which may be called in a' general way arguments from analogy: 
the enthymeme (in Aristotle's sense), analogical induction, the 
example and certain inferences drawn from the theory of proba- 
bilities; under another heading, the hypothesis; under a third, 
the argument from authority. 



FORMAL I MSI ( IF LI >GIC \l. ORDER 

71. I. Arguments from Analogy: i I i The Enthymeme.— The 
enthymeme, says Aristotle, is "a syllogism drawn from certain 
resemblances or certain marks." — The "marks" here meant, it 
must be understood, arc not the natural properties of the subject. 

Such reasonings arc very frequent in ordinary life. E. g. : 
Mosl men act from self-interest. Therefore, in this case, Peter 
acted from self-interest. 

72. I 2 ) Analogical Induction or Analogy. — Scientific induc- 
tion, with which we shall deal later on, disengages from among 
the many various accidents of a substance a natural property, and 
concludes with certainty that this property is the foundation of 
a general law. 

Analogy is a reasoning of the same nature as induction, hut it- 
conclusion is only probable. 

We employ analogical induction, or analogy, when, having 
recognized in two objects or phenomena certain characteristics 
which are really common, we infer that one or more other, here- 
tofore unknown, characteristics of these object- or phenomena 
must likewise be the same. 1 

73. (3) The Example. — Induction, whether scientific or ana- 
logical, moves from the fact to its sufficient natural reason, to 
its law and. by consequence, to the universality of its applications. 

Example moves in a conjectural way from one particular case 
to another particular case. 

i I ) Probable hypothe-es and conclusion- drawn from the 
theory of probabilities. 2 

74. II. Arguments from Authority. — In many circumstances 
of practical life men allow themselves to be guided by others, 
and they obey arguments from authority. 

The affirmation of an authority may bear upon a fact or upon 
a doctrine; in either case its logical value is probability. It is 
certain that a legitimate tendency inclines us to place reliance in 
a general way on the exactitude and sincerity of our fellow-men. 

Nevertheless, confidence in the statement of another cannot 



' Analogy is abused in the sciences either by exaggerating resem- 
blances to suit one's purpose, ignoring differences, or by taking a metaphor 
for a resemblance. 

2 See 95. 



56 LOGIC 

reasonably be absolute. A man who had never before lacked 
prudence and circumspection in his observation of external facts 
might, in this one instance, have acted inconsiderately. An 
habitually sincere man may have lied in this case. 

In each particular case the argument from authority has its 
value; but no human testimony justifies absolute certainty. 

In a doctrinal affirmation, St. Thomas does not hesitate to de- 
clare, the argument from authority is the weakest of all : "Locus 
ab auctoritate, quae fundatur super ratione htimana, est infirmis- 
simus." 

This declaration is a crushing answer for those superficial 
minds who would make Scholasticism an abdication of the per- 
sonal reason in favor of authority. 



Erroneous and Sophistical Arguments. 

75. False Reasoning. — Error proceeds from the basis or from 
the form: from the basis when we take for true and certain 
premises which are erroneous or doubtful; from the form- when, 
consciously or unconsciously, we draw from the premises a con- 
clusion which does not logically flow from them. 

In the former case the false reasoning is called an erroneous 
argument ; in the latter case it is called a paralogism or a soph- 
ism. The paralogism is a false reasoning of which we ourselves 
are the dupes ; the sophism, hr the current acceptation, implies 
the intention of deceiving. 

76. False Reasonings or Sophisms. — With Mill we may divide 
sophisms into two classes : 

(1) Sophisms of simple inspection, or a priori sophisms. 
These are prejudices, that is, maxims generally accepted without 
argument, which, therefore, no one doubts, and which, neverthe- 
less, are erroneous or at least equivocal. 

Example : To lay down as a principle that the logical order 
must correspond with the ontological^-"ideas with things". This 
preconceived dogma is one of the supports of Pantheism. — To 
repudiate a priori one or more means of knozving and then to 
pronounce absolutely unknowable whatever eludes the one means - 
of knowing- which has been arbitrarily set aside. This prejudice 



I I iRM VL CAUS] i >i LI »GTC \l. I IRDER 

enables Rationalism to deny all revelation.— To affirm without 
v v thai man is entitled to unbounded liberty. 

i 2 i Sophisms in reasoning properly so called, or sophisms of 
infer, 

Of these some are sophisms of induction; others, of deduction. 
comprising sophisms in terms and in form. 

77. False Reasonings Properly So Called. — I. Sophisms of 
Induction. — Under this head arc included all sophisms which 
arise in inductive reasoning, whether they affect the preliminaries 
(sophisms of obsecration) or the inductive reasoning itself 
(sophisms of interpretation, or of inductive inference). 

(1 ) SopJiisms of observation. — Patient and honest observation 
is the starting-point of all inductive research. Too often, how- 
ever, eagerness to reach a conclusion drives the investigator into 
assertions which go beyond the bounds of his observation. 

(a) We see zvhat we wish to see, instead of seeing what is. 
Example: Haeckel's primary monerons and Huxley's famous 
Bathybius. 

( /' i We do not see what we wish not to see. Example: The 
biological theories which would demonstrate the identity of the 
animal and the vegetable cell. 

(2). Sophisms of interpretation. — Those which consist in 
wrongly interpreting observed facts. The observation is com- 
plete, but the meaning attributed to it is added by a suggestion 
arising from the eagerness to form a complete system. 

Example : To conclude from the fact that forms of energy 
may be expressed in terms of mechanical energy to the thesis 
that all corporeal energies — including those developed in nervous 
tissue, and accompanied by sensation, passion, spontaneous move- 
ment, or by thought and volition — are nothing but mechanical 
energies. 

(3) Sophisms of inductive inference, or of induction. — The 
example is illegitimately employed when we pass from one ob- 
served case to another without first taking care to connect both 
of them by means of induction with a natural cause. Ab uno 
disce omues. The analogy is abused in the same way. 3 



1 Certain sophisms of induction may be classified indifferently in 
■several of the groups of hasty generalizations. 



58 LOGIC 

78. II. Sophisms of Deduction. — (1) Sophisms of terms. — 
These are connected with the signification of words which are 
changed, distorted out of their true sense, or taken in several 
different senses. The principal ones are : 

(a) Equivocation, or ambiguity of terms. This consists in 
employing a word in a double sense in reasoning, or taking an 
ill-defined word in two different acceptations. Example : The 
use of the terms, liberty, equality, solidarity, evolution, rational- 
ism, liberalism, socialism, etc. — Equivocation introduces a fourth 
term into the reasoning. 

(b) Passing from the collective to the separate sense (fallacia 
compositionis). This sophism consists in affirming of things col- 
lectively what is true only of those same things taken separately. 
As when Christ says, in the Gospel : "The blind see ; the lame 
walk upright ; the deaf hear" ; this can only be true taking these 
things individually, not comprehensively. 

(c) Passing from the separate to the. collective sense (fallacia 
divisionis) . This consists, on the contrary, in taking the collec- 
tive sense. E. g., if we should argue : Five is o.ne number ; but 
two and three make five ; therefore two and three make one 
number. 

(2) Sophisms of inference or of "deduction." — (A) The 
petitio principii is when we begin by supposing the very thing 
which is in question. This sophism is committed when we take 
for granted: (a) the very thing that has to be established; (b) 
the whole, when a part of it remains to be proved; (c) a part of 
what has to be proved as a whole; (d) each one of the parts of 
the whole that has to be established; (<?) a point of doctrine 
necessarily bound up with the principle in question. 

(B) The vicious circle is an aggravation of the same sophism: 
it. not only takes for granted what is in question, but it proves two 
propositions one by the other reciprocally. E. g., Descartes 
proves God's veracity by the evident character of truths, and the 
same evident character by God's veracity. 

(C) The sophism of accident confounds (a) what is acci- 
dental with what is essential, or (b) what is relatively with what 
is absolutely true. As when a thing is condemned absolutely be- 
cause of certain abuses to which it gives occasion. 

(D) The sophism of non-cause confounds concomitance or 



It IRM \l. C MSI. OF LOGIC \l. ( IRDER 50 

succession with the relation of causality: with this, therefore, 

because of this; or, after this, therefore because of this •• again, 

mitance with identity: with this, therefore this itself. 

i /' i Connected with this sophism is the confusion of condition 
with cause, or of partial with fota/ cause. 

i E) The sophism of interrogation consists in joining together 
several questions which are really distinct, as if they all demanded 
a single reply. As: Why did you kill your wife? — This interro- 
gation supposes already settled the preliminary question: Did 
kill 3 our wife? 

i F i Ignoring the state of the question, ignoratio elenchi. This 
sophism takes three forms: the reasoning proves too much, or 
too little, or it proves something apart from what is required to 
be proved. 3 

ARTICLE III. 

Scientific Systematization. 

Preliminary. 

79. Science is a System. — The organic growth of science is 
gradual. Concepts take their places in judgments; judgments, in 
reasoning. Demonstrative reasoning produces a fragment of 
science. Reasonings are co-ordinated and subordinated, and the 
orderly whole forms a science. 

A science is an assemblage of propositions which form a 
avar-qfia — a whole which stands up by itself. 

It is its formal object that gives a science its unity. 

The definition of the essence of a thing gives rise to certain 
simple and general initial propositions — the principles of the 
science — from which reason deduces certain conclusions. These 
first conclusions lead to others, dependent on them, and, through 



i To this list of the commonest sophisms may be added the paradox. 
This is a judgment which contradicts a common opinion. The latter 
may be true or false. Hence, there are two classes of paradoxes, of 
which only the first deserves to be so called. To maintain that all in- 
telligences are equal (Helvetius) is a genuine paradox. — To say that it 
is better to suffer wrong than to do it, at first seems paradoxical, but is 
not really so. The paradox is sometimes a mere joke or an ill-natured 
sarcasm, and is thus of no particular importance. 



60 LOGIC 

them, subordinate to the principles; so that the whole scientific 
structure is based upon principles furnished by the analysis of 
the subject. 

The systematization of science is the supreme intrinsic purpose 
of logic. 

80. Scientific Systematization.— There are three factors of 
this (tres modi sciendi — three modes of knowing): definition; 
demonstration ; division. 

Definition furnishes the principles ; demonstration passes from 
principles to conclusions. While the definition says what a thing 
is, it shows in what that thing differs from things of another 
species comprised in the same genus. Thus differentiation, or 
division, is the auxiliary of definition. 

Having studied the function of definition and division, and the 
conditions under which they are employed (§1) (demonstration 
has already been sufficiently treated) we shall enquire how 
these factors adapt themselves to the various sciences, and to phi- 
losophy : the study of method in general and of the methods re- 
spectively appropriate to the various groups of sciences (§2). 

§ 1. Scientific Processes. 

81. I. The Function of Definition. — To define is to say what 
a thing is. — Definition has a twofold function : 

(1) The accessory function of clarifying concepts by resolv- 
ing things that are to be known into their elements, so as to 
obtain a better light on them. 

(2) The essential function of laying the foundations of science. 
Just as not everything can be demonstrated, so not everything 

can be defined. Passing from analysis to analysis, we must 
sooner or later end with notions not susceptible of analysis. Such 
are the notions of unity and of number, the basis of arithmetic. 
These notions furnish the materials of the definitions, or first 
principles, on which the whole science rests, as a building rests 
on its foundations. 1 



1 "The principles of the sciences are indemonstrable definitions. The 
definition manifests what a thing is; thus mathematics lays down as 
principles what unity is, what an uneven number is, and so on." Aristotle, 
Posterior Analyt., II, 3. 



1 i IRM \l. < UJSE ( >F Li IGIC \l. < »RDER 61 

82. Definitions of Words and Definitions of Things.— i L) 
The verbal definition explains the signification, etymological or 
conventional, of a word. Its purpose is to make our ideas clear 
and avoid equivocation. 

(2) The real definition says what a thing is. The real defini- 
tion is essential, natural, or descriptive. 

(a) Essential definition. — To know in a perfect manner what 
a thing is, is to know its intimate nature, its essence. Xow the 
individual essence, by reason of which this individual subject is 
what it is, distinct from other individuals, is unknowable to 
man. 1 We know only by classes. 

i /> ) Accidental definition. — Wither do we immediately attain 
the generic or specific essence. On observing the qualities of be- 
ings, we do not even know, at first, whether they are natural or 
accidental; the designation is often only a description, improperly 
called a descriptive 'definition. 

It is accidental when it designates a thing by means of acces- 
si iry notes the whole sum of which belongs to this thing alone. 

(c) Natural definition. — When, through induction, the mind 
comes to discern in the thing one or more necessary qualities, it 
defines the thing by its properties: this is natural definition. 

The definitions used in chemistry, mineralogy, botany, zoology, 
etc.. are descriptive, accidental, or at most natural. 

The essential definition, then, is an ideal, which is but rarely 
attained. And yet, it alone is rigorously scientific or philosophic. 

How do we form it? 

83. Processes of Definition. Synthesis. Combined Analysis 
and Synthesis. — Some sciences are rational, others, exact or ex- 
perimental sciences, accordingly as their principles are rational or 
supplied by induction. 

The process of definition in the rational sciences is synthetic; 
in the experimental sciences it is first analytic and then synthetic. 

(1) Rational sciences.— By means of ordinary observation we 
abstract from reality as perceived by the senses certain very sim- 
ple notions (decomposition) which we then combine into more 
and more complex objects (synthesis). Each of the notes put 
into the synthesis is more universal than the object of the syn- 



1 See Psychology. 



62 LOGIC 

thesis, but their totality is 'more limited than each of them by 
itself: synthesis progressively limits its object, and makes its 
definition (opos 6pt.o-iJ.6s). 

Example : Three is the first uneven number. Each of the attri- 
butes belongs to other numbers; but their combination limits 
their attribution to the number three : they define it. 

As the comprehension of the concept increases, so its extension 
diminishes. Synthesis, then, is a direct process of definition. 
We shall see later on that it is at the same time an indirect 
process of elimination — of division. 

The attribute uneven is opposed to the attribute even; it ex- 
cludes the number two. The attribute first excludes all the num- 
bers except two and three. So then, the combination, first, un- 
even excludes all the numbers except three. The definition, first, 
uneven number, fits the defined object, three, and no other object 
— it is adequate. 

(2) The experimental sciences end their work with a syn- 
thesis ; but they begin with an analysis. 

To arrive at a definition of life, we begin by observing the 
various beings which are called living, and look for something in 
them to justify a common attribute. 

When we eliminate in thought that which distinguishes some 
of the various vital acts from the rest (nutrition; cognitions; 
appetitive acts, whether sensual or intellectual), we find in them 
a common characteristic: they are immanent. 1 Immanent ac- 
tivity is the definition of life. 

Division — elimination of distinctive notes — has brought us to 
definition. And definition will bring back again the division from 
which the analysis began. 

Vital immanence is, in fact, found with specific differences in 
nutrition, in sensations, and in appetitive acts whether sensual or 
super-sensual. Science descends again from genus to species, 
from simple to composite. 

This alternation of analysis and synthesis, moreover, will be 
prolonged. Side by side with the forms of immanent activity 
there are forms of transitive activity; the mind abstracts their 
common characteristic, activity ; this is the generic element, im- 



1 See Psychology. 



Fi IRMAL CAUSE OF L( >GIC \l. I >R1 > G3 

manence is a distinctive note. And the two notes combined Eorm 
the definition of life, the combination of a notion of kind with a 
notii 'li of difference. 

Thus, through all these species, analysis pursues a genus which 
is wider and wider, then a type more and more simple, until it 
arrives at elements not to be analyzed, by means of which those 
first definitions arc formed which arc the generating principles 
of the sciences. 

This shows how important is the part played by definition in 
science. In the experimental or exact sciences, as well a> in the 
rational sciences, to define is to break a thing up and take hold 
of its simplest determinations, so as to again identify it with 
these elements (synthesis). The least comprehensive — and 
therefore most extensive — determination is the generic clement 
of the definition ; that which complements the generic elements — 
which delimits the concept, and hence is peculiar to, and specific 
of. the thing defined — is called the specific difference. 

Science, however, is in the end always the same: it makes 
effects known by their causes, consequences by their principles. 

84. Rules of Definition. — These relate to the twofold function 
of definition. 

I. First point of view: The definition must furnish the first 
principles of the science. Hence the following rules : 

(1) The definition must proceed from an object antecedent 
to the thing defined. Consequently : 

(a) Correlative terms (as health and sickness), being simul- 
taneous, cannot be used to define each other. 

'(&) Different members of a division are not defined by one 
another. 

(c) A thing is not defined by itself or by that to which it is 
antecedent. 

(2) The genus used in the definition must be the nearest 
genus. 

II. Second point of viezv: The definition should help to clear- 
ness of ideas. It must be clearer than the thing to be defined. 
Consequently, it must: 

(a) Not repeat the name of the thing to be defined. 

(b) Avoid metaphorical, ambiguous, and obscure terms. 

(c) Be concise and adequate. 



64 LOGIC 

85. II. Division Inseparable from Definition. — The processes 
of definition and division go hand-in-hand and complete each 
other. 

The definition says what a thing is, identifies it with the simplest 
components of its essence (genus and specific difference). The 
division shows to what special forms the generic element of the 
thing defined applies. The genus is the foundation, or reason, of 
the division. 

(1) In the exact sciences the reasoning faculty sets out from 
generic notions, follows the progress of their specialization, and 
at every stage marks a new division or subdivision of the genus 
into subordinate species. In the example given in 83 (1) the 
number is first specialized as uneven, then it is individualized by 
the exclusion of all other uneven numbers which is involved in 
the attribute first. 

(2) In the positive sciences the reasoning faculty at first fol- 
lows the inverse process, the analytic: here division brings us to 
definition. We observe distinct activities in vegetable, animal, 
and human substances ; nevertheless, at the basis of these activi- 
ties, there is a common activity : immanent activity, or life. The 
two different forms of activity— 'the transitive and the immanent 
— in their turn cover a common idea — a higher genus — activity. 
Step by step the mind passes from species to genera, from the 
members of the division to the reason of their separability. 
Nevertheless, when the common principle is disengaged, the 
mind turns back to the subjects analyzed to comprehend syntheti- 
cally the formal divisions of the genus into its species. 

Definition and division, then, are indissolubly joined together. 
In the exact sciences the definition precedes, the division follows. 
In the experimental sciences a first superficial division leads 
to the essential difinition ; the latter in its turn becomes the 
formal reason of the specific differences observed in the first 
instance. 

86. Rules of Division. — Like definition, division plays a two- 
fold part : one, fundamental, in the scientific order ; the other,, 
secondary, in the pasdagogic order. 

I. From the first point of view the rules of division are : It must 
be complete; rationally progressive ; if possible, positive. 

II. In a second point of view, the division is made for the 



FORMAL CAUSE OF Li IGICAL ORDER 65 

orderly arrangement and clarification of concepts. For this pur- 
pose il must In- complete, clear, and methodical. ' 

§ 2. Method and Methods 

87. Method. — Diversity of Scientific Methods. — Method 
(ntdoSos) means road; a scientific method is the road which 
leads to a science. 

It varies with the nature of the various sciences to which it 
leads: synthetic or analytic accordingly. Still, it may he said that 
the scientific method is on the whole a mixed one, analytico-syn- 
thetic- 

This section will treat of the respective methods of (I) the 
abstract sciences, (II) the experimental, (III) philosophy. 

88. I. The Synthetic Method. — An exact, or deductive science 
— such as arithmetic or geometry — sets out from certain princi- 
ples in necessary matter and combines them to deduce new rela- 
tions and to form the definitions of the object with which the 
science concerns itself. It passes from the simple to the com- 
plex, from the more general to the less general. This is the syn- 
thetic method. The synthesis which directly forms a definition 
at the same time effects the division of the defined object and 
governs all rational demonstrations. Let us suppose, e. g., these 
theorems established: (1) that the sum of the angles comprising 
all the space below a straight line is equal to two right angles ; 
(2) that the interior alternate angles are equal ; that a straight 
line can always be drawn parallel to a given straight line. — The 
combination of these three propositions under the guidance of 
the principle of identity gives rise to a new relation: the identity 
of the three angles of a triangle with two right angles. 

89. II. Method of the Positive Sciences. Its Object.— The 
positive or experimental sciences begin from concrete facts and 
end by formulating laws. They go from the complex to the sim- 
ple, from the particular to the general — the analytical method. 



i The authors of Port Royal point out that it is "equally a defect to 
make too few and too many divisions; the one does not sufficiently en- 
lighten the mind, the other dissipates it too much.*' 

2 The analytico-synthetic are the constructive methods of science. 
Nothing will be said here of the methods of teaching, the didactic methods. 
See Higher Course, vol. I. 



66 LOGIC 

Though the happenings of nature are variable, the most super- 
ficial observation shows that this variability is dominated by cer- 
tain constant and general laws : to determine the laws of these 
happenings and the nature of things known by experience is the 
object of the sciences of observation. They begin from the ob- 
servation of complex and variable facts in order to separate from 
them the simple element and the permanent law: this procesS'Of 
de-composition (analysis), considered as a whole, is called induc- 
tion. Hence the expresion, inductive sciences, as opposed to the 
deductive, or rational, sciences. 

90. Stages of the Inductive Process. — To perform an induc- 
tion is to ascend from effects to their cause, to determine the 
properties, and, through them, the nature of the cause, in order 
to understand the law of its action. Induction comprises four 
stages : 

(1) The observation of certain facts which are presented to 
the senses. E. g., the chemist observes, a certain number of 
times, in dissimilar circumstances, that different absolute quan- 
tities of hydrogen (H) and of chlorin (CI) have combined to 
form a definite body (HC1). 

(2) The hypothesis. — The investigator supposes that the ob- 
served phenomenon is inexplicable by constantly recurring fortu- 
itous coincidences, and that it must have a sufficient reason in the 
nature of reacting bodies. 

A scientific hypothesis is the provisional explanation of certain 
observed facts. x 

(3) The verification of the hypothesis, which is the heart of 
the inductive process, is effected sometimes by simple observa- 
tion, sometimes, in a decisive manner, by experiment. 

(a) By observation. The author of an hypothesis imagines 
the results that should follow if it were verified and found to 
operate in nature. 

(b) By experiment. The observer is not merely a witness of 
the course of events in nature, but himself influences those events. 
By artificial means he varies, according to the aim which he has 
in view, the agents which operate in a complex phenomenon. 

(4) The deduction. — The property of the bodies CI and H. to 

1 See the thorough study of hypothesis in the Higher Course. 



M IRM \l. I \l SI ( IF LI >GIC \l. ' IRDE R 

combine in the definite proportions of l and 35.5, once recognized, 
the reasoning faculty goes further and from its verified observation 
draws a general conclusion: thenceforward, every time II and CI 
arc mixed in the proportions of 1 and 35.5, and exposed to the 

action of the sun's rays, hydrochloric acid will be formed, and 
22 calories per molecule-gramme will be liberated. 

The consideration of these several stages raises various ques- 
tions: I 1 ) the observation of facts and their -verification by ex- 
periment belongs to the description of the methods of induction; 
(2) the generalization of the observed fact raises the question of 
the basis of induction; (3) as to deduction, or the last stage of 
induction, we shall note the relations between deduction and 
induction. 

91. Inductive Methods. — Following Mill's terminology, these 
are the methods of agreement, of difference, of concomitant -vari- 
ations, of remainders, and the composite method. The first three 
are the principal ones. 

(1 ) Method of agreement: When the phenomenon, the nature 
of which is to he determined, has occurred in several different 
cases, and these different cases have a single circumstance in 
common, this common circumstance is probably the sufficient rea- 
son of the phenomenon. 

(2) Method of difference: Two cases are observed: in one 
the phenomenon occurs, in the other, it does not; all the circum- 
stances of the two cases are identical except one, which is present 
in the first case and absent in the second. It may be inferred 
that tins one circumstance is the whole or partial sufficient reason 
of the observed phenomenon. 

( ."> ) Method of remainders, a composite method, produced by 
a modification of the methods of agreement and of difference: 
When the part known to result from certain antecedents, already 
determinerl by previous inductions, is eliminated from the 
phenomenon, then what is left of the phenomenon is caused by 
tlie remaining antecedents. 

| I ) Method of concomitant variations: When the degrees of 
variation of a phenomenon correspond with the degrees of varia- 
tion of a given antecedent, it is to lie presumed thai there is 
beteewn the two a relation of causality, immediate or mediate. 
This method, Mill" observes, is particularly demanded when in 



68 LOGIC 

all the cases the preceding methods are inapplicable, as happens 
when the cause of the phenomenon cannot be completely isolated. 
(5) The composite method is the cumulative employment of 
all the preceding. 

92. The Object of Induction. — The experiments which deter- 
mine the law of a chemical combination reach the formal cause 
of the body, since they reveal the properties springing from that 
formal cause. These same experiments also determine the 
material cause of chemical compounds, because they determine 
the proportional quantities of the components. They may also 
regard the final cause of the combinations, or the tendencies, in 
pursuance of which the combinations are formed. 

Nevertheless, whatever cause in particular may be sought by 
these researches, they have one object: to determine a property 
and, by means of it, the specific nature of a being, and, conse- 
quently, the laiv of its action. 

We may say, then, that the object of inductive researches is 
sometimes the discovery of causes (proof of fact, on.), some- 
times — and more profoundly — the discovery of natural laws and 
the definition of the types of nature (demonstration, Sioti). 

The. nature of the being is revealed by its properties ; on them 
its laws are based. 

Note that inductive conclusions pass through different degrees 
of generalization. 

93. Logical Foundation of Induction. — The problem is usually 
stated as follows : Induction passes from the fact to the law,. 
from some observed cases to all observable cases. Why is this 
process legitimate? Because the concurrence of a large number 
of variable elements and forces in one harmonious and persistent 
combination (the fact established by observation and experi- 
ment) demands its sufficient reason. Now this sufficient reason 
can only be a natural inclination of the bodies in which the har- 
monious and stable combinations take place. This thesis has 
been demonstrated in Criteriology, n°. 63. 

94. The Induction and the Syllogism. — The scientific 1 induc- 
tion does not differ from the syllogism. By means of the induc- 



1 We are not concerned here with the complete induction, which is 
not scientific. See Hisher Course. 



Im IRM \l- C \l'SE OF LOGICAL ORDER 69 

tive method, indeed, the cause of the observed phenomenon is 
made manifest. The inductive methods reduce to those of agree- 
ment and of difference, both of which are applications of the 
conditional syllogism. Furthermore, when, by means of induc- 
tive methods, it has been established that the presumed cause 
of the phenomenon is its true cause (demonstration on), it is 
shown that this cause is not indifferent, but is naturally deter- 
mined to the manifestation of a certain property, to act in con- 
formity with a law. And this demonstration, again, is expressible 
in syllogisms. 

95. Statistics. Their Relation to Induction. — Scientific in- 
duction concludes with certainty to the existence of a definite 
law of nature. Xow we are often brought face to face with 
facts evidently governed by laws, the intricacy of which the mind 
does not fathom. We then have recourse, provisionally, to the 
registration of these facts and their coincidences. This con- 
stitutes the object of statistics. 

Statistics are an inventory of numerous facts in which their 
relative frequency and their coincidences are noted with the 
view of discovering indications of natural causes. 

It is beyond doubt that there must be a sufficient cause, in the 
very nature of things, for this constant recurrence of events, but 
we do not know, or eren guess, with what natural properties this 
law is connected. 1 Just as soon as the observer guesses, out 
of all this heap of facts, what invariable conditions (method of 
agreement), which are also exclusive (method of difference) 
and correlative in point of intensity (method of con- 
comitant variations), are antecedent to the event to be explained, 
so soon will he enter upon a science. A scientific hypothesis will 
have emerged. The verification of the hypothesis will be the 
work of induction. 



] There are cases where the facts show neither the regularity nor the 
constancy- which indicate a law, e.g., A homogeneous die, with one of the 
numbers from 1 to 6 on each of its faces, is thrown. In 12 throws, the 
numbers 3 and .5 have each turned up three times; the 2 and the 4, twice; 
the 1 and the f> only once. The probability of contingent events may be 
submitted to calculation and affords opportunity for interesting applica- 
tion-. For the theory of probabilities and its logical value. Bernouflli's 
theorem, and Poisson's law of higher numbers, see Higher Course, vol. I. 
pp. 352 sqq 



70 LOGIC 

96. III. The Analytico-Synthetic Method. Conclusion. — Two 

scientific methods are commonly distinguished : that of the exact 
sciences, synthesis; that of the sciences of observation, analysis. 
Synthesis is indeed the basis of the first of these groups of 
sciences, and analysis of the second ; but neither character- belongs 
exclusively to either group. 

The axioms which lie at the basis of the exact sciences in- 
evitably rest upon certain elementary observations. 

The results obtained by analysis and induction in the positive 
sciences prepare the material for synthetic deductions. All 
science, in fact, aims at the knowledge of things by their causes. 
The demonstration propter quid alone is rigorously scientific. 
Even the particular sciences, which have nature for their object 
(e.g., mechanics, optics, chemistry), endeavor to link their con- 
clusions with mathematics and metaphysies. 

Finally, then, the only scientific method is inductivo-deductive 
and analy 'tic o -synthetic. 1 

97. The Method of Philosophy. — The same analytico-'synthetic 
method rules in philosophical speculation. 

As philosophy is the science of being in general — of all being 
— it embraces both the ideal and the empirical order. It passes 
through both analytically, in order thereafter to explain both 
synthetically. In this sense we define it, with Aristotle, as "the 
knowledge of things by their most profound reasons", or as "the 
profound knowledge of the universal order." 

In each of its parts (physics, mathematics, metaphysics) 
philosophy uses the analytico-synthetic method. 

(1) The physics of the ancients is nowadays divided into 
cosmology and psychology. By the aid of the physical, chemical, 
and mineralogical sciences, cosmology leaches the general induc- 
tive conclusions that corporeal substance is composed of matter 
and form, and exerts certain proper and characteristic activities. 
By means of these principles philosophy explains synthetically 
both the movement of corporeal nature, and the diversity, as well 
as the constancy of the laws which govern it. 



1 After these notions of general methodology, it would be in place, 
in special methodology, to determine the method proper to each science. 
On this subject we recommend De la mcthode dans les sciences, by vari- 
ous professors, Paris, Alcan, 1909. 



IRM \l. i \l'SK I >!• Li IG1C \1. < >RDER 71 

In psychology, facts warrant the inductive conclusion that the 
first sjubjecl of human life is a material compound informed by 
an immaterial soul. This conclusion, the principle of synthetic 
psychology, enables us better to understand the proper object of 
human reason, the complexity of psychological life and the 
interdependence of its divers manifestations. 

(2) The philosophy of mathematics is, in fact and of right, 
bound up with mathematical sciences. The mathematicians have 
never separated their theorems from the axioms whence they are 
deduced. Certain rudimentary observations suggest the axioms, 
the principles of the syntheses which form the sciences of number 
and of quantity, and lead on to the most abstract speculations of 
pure geometry. 

(3) The various parts of the philosophical sciences lead to 
indefinable objects: physics, to substance composed of potential- 
ity and act. of matter and form — to movements produced in a 
passive subject by an efficient cause determined by an intrinsic 
end, mathematics, to the one, to the discreet, to addition, to num- 
ber, etc., or to continuous quantity, as the line, the surface, etc.; 
criteriology. to the true; ethics, to the moral eml, to moral good; 
lastly, logic, to the being of reason, to the orderly arrangement 
of the objects of the reasoning faculty. The first philosophy, or 
metaphysics, takes for its object these indefinable entities and 
their relations, and these are the point of departure of the general 
synthesis which constitutes, in the formal and strict sense, rational 
wisdom, or philosophy. 

The ideal of philosophy would be the power to explain the 
universe, its elements and its laws, judging it, as it were, from 
above, by means of a synthetic knowledge, as perfect as our 
nature can attain, of the First Cause Who has created the world 
by an act of His almighty power, and continually governs it by 
His providential wisdom: the "synthetic return.'* or study of the 
world in its First Cause is the summit of philosophy. 1 



i Thu- we see how the circular demonstration differs from the vicious 

circle. 



CHAPTER IV 

Final Cause of Logical Order. 

Conclusion 

98. Logic in the Service of the Knowledge of Truth. — The 

order, or. internal systematization of the judgments and reason- 
ings which constitute a science, is the intrinsic aim of logic. 

But logical order, as such, does not ensure the attainment of 
truth, the final aim of the human mind. This is why the ulti- 
mate aim — extrinsic, it is true — of the logician is the certain 
knowledge of truth, which alone deserves the name of science. 

99. Definition of Science. — Science may be defined : A group- 
ing of evident and certain, necessary and universal, systematically 
organised propositions, which are drawn immediately oj medi- 
ately from the nature of the subject, and give the intrinsic reason 
of its properties and of the laws of its action. The propositions 
of a science must be : 

(1) Objectively evident, i. e., manifestly true. 

(2) Certain. An object of faith is, by definition, formally in- 
evident; it is not, as such, an object of science. Scientific certi- 
tude is the outcome of systematic thought. 

(3) Necessary and universal. To gather particular facts is 
not the work of science ; at most it is preparatory to it. The man 
of science seeks to know zvhat things are independently of their 
contingent and variable circumstances — what is the law of their 
action. "There is no science but the universal", is Aristotle's 
favorite theme. 

(4) Systematic, organised. Science is a unified whole. The 
unity of science, considered formally, consists in this : that its first 
definitions lay down the principles from which, by synthesis, all 
the following propositions are deduced. These generating prin- 
ciples are based upon' the formal object of the particular science. 
That object is, if not the essence, at least a natural property, of a 
real subject. Consequently, the intimate reason of the unity of 
the science is the essence, the nature, to ri eo-n, of its object. 

This unity is the ideal of a perfect science. 



TABLE OF CONTENTS 



INTRODUCTION 



No. 

1. Definition of logic 

2. Materials of logical order 

3. Formal cause of logical order 

4. Difference between psychology and logic 

5. Final cause of logical order 

6. Difference between logic and metaphysics 

7. Logic may be regarded as a practical science or as an art 

8. Divisions of logic 



Page 
3 
3 
3 
4 
4 
5 
6 
7 



CHAPTER I 



Efficient Cause of Logical Order 



9. Origin and nature of the operations of the reasoning faculty . S 

10. Multiplicity of the operations of the reasoning faculty. Their 

fundamental identity 8 

11. The abstract character of concepts renders judgment and 

reasoning possible 10 



CHAPTER II 
The Matter or Material Cause of Logical Order 



12. Object and division of Chapter IT 



11 



ART. I. CONCEPTS 

§ 1. The concept, its abject and properties 

13. The concept in its logical aspect 

14. By what right does logic concern itself with acts of mere appre- 

hension 

15. Logical problems raised by the act of mere apprehension 

16. Logical categories or predicaments .... 

17. The predicables 

18. Comprehension and extension of concepts 

73 



11 

n 
12 

13 

14 
16 



74 LOGIC 

No. Page 

19. Relations of subordination between ideas in respect of their ex- 

tension . . . .... . 1? 

20. Comparison of ideas in respect of their comprehension. Relation 

of identity and opposition 19 

8 2. Division of concepts 

21. Principal heads of classification of concepts . . . . 19 

22. Classification of ideas in respect of the object abstracted by the 

intellect 20 

23. Classification of ideas in respect of their way of representing 

the object 21 

24. Classification of cognitions in respect of their origin or their 

formation . . ' . . . 21 

ART. II. TERMS. 

8 1. The term, its object and properties 

25. Object of the term 22 

26. The ten parts of speech ......... 22 

8 2. Classification of terms 

27. Classification of terms . . . . . . . . . 23 

CHAPTER III 



The Formal Cause of Logical Order 



28. Preliminary note .......... 25 

ART. I. JUDGMENT AND PROPOSITION 

§ 1. Notion of the judgment and the proposition 

29. The judgment and the proposition 25 

30. Function of judgments and propositions in the intellectual life . 26 

§ 2. Judgments and propositions 

31. General classification of propositions 26 



I. CLASSIFICATION OF SIMPLE PROPOSITIONS 

32. First division of propositions : In respect of their matter 

33. Two kinds of judgments in necessary matter 

34. Synonymous designations of the foregoing 

35. Second division of propositions : In respect of their form 

36. Logical value of the predicate of a simple proposition 

37. Third division of propositions: In respect of their quantity 

38. Fourth division of propositions : In respect of their quality 



27 
27 
29 
29 
30 
31 
32 



CON! ENTS 



Mb 



II. CLASSIFICATION 01 COMPLEX PROPOS] 

39. Classification of complex propositions .... 



;< 3. Relations betoveen propositions 






40. Relations between propositions .... 

41. Equivalence of several propositions 

12. Convertibility of propositions 

4:5. Relations of opposition and subordination 

•li. Rules relating to the truth or falsity of opposed propo 

45. Rules relating to the truth or falsity of subordinate propositions 

46. Immediate inferences ....... 

ART. II. REASONING 

47. Preliminary remarks. Object of Art. IT 

§ 1. Reasoning ami the syllogism 

48. Reasoning ....... 

49. The syllogism. Terminology 

50 .Nature and logical basis of the syllogism 

51. Of what order is the necessity of the principles of the syllogism? 

52. Logical first principles 

53. Figures and modes of the syllogism 

54. Rules of the syllogism 

55. Range of the rules of the syllogism. Logic and truth 



75 



34 
34 

34 
35 

36 

157 
37 



§ 2. Syllogisms 



56. Preliminary remarks 



37 



38 
39 
40 
41 
41 
42 
42 
45 



47 



I. SYLLOGISMS CONSIDERED AS TO THEIR FORM 



57. Division of syllogisms in regard to their form 

58. Variety of the categorical syllogism 

59. Nature and rules of the conditional syllogism 

60. The conjunctive and the disjunctive syllogism 

61. The exclusive syllogism 

62. The dilemma 



47 
47 
48 
49 
49 
50 



II. SYLLOGISMS CONSIDERED AS TO THEIR MATTER 

63. Preliminary remarks 



51 



76 



LOGIC 



DIFFERENT KINDS OF DEMONSTRATION 

No. 

64. I. Primary Division 

65. Conditions of a scientific demonstration 

66. Proof of fact and causal demonstration 

67. II. Demonstrations a priori and a posteriori 

68. III. Circular or retrogressive demonstration 

69. IV. Other accidental forms of demonstration 



Page 
51 
52 
52 
53 
53 
54 



PROBABLE ARGUMENTS 



70. Probable arguments 

71. I. Arguments from analogy: (l) The enthymeme 

72. (2) The analogical induction,, or analogy 

73. (3) The example 

74. II. Arguments from authority .... 



54 
55 
55 
55 
55 



ERRONEOUS AND SOPHISTICAL ARGUMENTS 



75. False reasoning . . . 

76. False reasonings or sophisms . 

77. False reasonings properly so called 

78. II. Sophisms of deduction 



I. Sophisms of induction 



56 
56 

57 
58 



ART. III. SCIENTIFIC SYSTEMATISATION 

Preliminary Remarks 



79. Science is a system . 

80. Scientific systematisation 



59 
60 



§ 1. Scientific processes 

81. I. Definition. Its function . 

82. Definitions of words and of things 

83. Processes of definition. Synthesis. 

combined 

84. Rules of definition 

85. II. Division inseparable from definition 

86. Rules of division 



Analysis and synthesis 



60 
61 

61 
63 
64 
64 



8 2. Method and methods 

87. Method. Variety of scientific methods . 

88. I. The synthetic method .... 

89. II. Method of the positive sciences. Its object 
90 Stages of the inductive process 

91. Inductive methods 



65 
65 
65 
66 



CONTENTS 



77 



Xo. 

92. Object of induction 

93. Logical foundation of induction 

94. The induction and the syllogism 

95. Statistics. Their relation to induction . 

96. Analytico-synthetic method. Conclusion 

97. The method of philosophy 



Page 
68 
68 
68 
69 
70 
70 



CHAPTER IV 



The Final Cause of Logical Order 



C( INCLUSION 

9S. Logic in the service of science and of truth 
99. Definition of science . . . 



72 

7;> 



THE MANHATTANVILLE PRESS 

110 WEST ELEVENTH STREET 

NEW YORK CITY 



THE MEANY PRINTING COMPANY, N. Y. 



SEP 13 1912 



' 



